Class 9 Physics Solution LAKHMIR SINGH & MANJIT KAUR by S. Chand Book School Books CBSE

Chapter 1: Motion

Very Short Answer Type Questions

1. Is displacement a scalar quantity?

Ans: Displacement is not a scalar quantity; it is a vector quantity.

2. State whether distance is a scalar or a vector quantity.

Ans: Distance is a scalar quantity.

3. Change the speed of 6 m/s into km/h.

Ans: The speed of 6 m/s is equivalent to 21.6 km/h.

4. What name is given to the speed in a specified direction?

Ans: The speed in a specified direction is called velocity.

5. Give two examples of bodies having non-uniform motion.

Ans: Examples of bodies having non-uniform motion include a car accelerating or decelerating and a person walking in a zigzag pattern.

6. Name the physical quantity obtained by dividing ‘Distance travelled’ by ‘Time taken’ to travel that distance.

Ans: The physical quantity obtained is speed.

7. What do the following measure in a car?

(a) Speedometer (b) Odometer

Ans: (a) Speedometer: Measures instantaneous speed.

(b) Odometer: Measures total distance travelled.

8. Name the physical quantity which gives us an idea of how slow or fast a body is moving.

Ans: Speed gives us an idea of how slow or fast a body is moving.

9. Under what conditions can a body travel a certain distance and yet its resultant displacement be zero?

Ans: When the body moves in a closed loop or returns to its starting point, the resultant displacement is zero.

10. In addition to speed, what else should we know to predict the position of a moving body?

Ans: To predict the position of a moving body, we also need to know the direction of motion, which is provided by velocity.

11. When is a body said to have uniform velocity?

Ans: A body is said to have uniform velocity when it covers equal displacements in equal intervals of time, regardless of the direction.

12. Under which condition is the magnitude of average velocity equal to average speed?

Ans: The magnitude of average velocity is equal to average speed when the motion is in a straight line.

13. Which of the two can be zero under certain conditions: average speed of a moving body or average velocity of a moving body?

Ans: Average velocity can be zero under certain conditions, even when the average speed is not zero.

14. Give one example of a situation in which a body has a certain average speed but its average velocity is zero.

Ans: If a car moves in a complete circle and returns to its starting point, its average speed over the entire journey may be non-zero, but its average velocity is zero.

15. What is the acceleration of a body moving with uniform velocity?

Ans: The acceleration of a body moving with uniform velocity is zero.

16. What is the other name of negative acceleration?

Ans: Negative acceleration is also known as deceleration or retardation.

17. Name the physical quantity whose SI unit is:

(a) m/s (b) m/s²

Ans: (a) m/s: Speed

(b) m/s²: Acceleration

18. What type of motion is exhibited by a freely falling body?

Ans: A freely falling body exhibits uniformly accelerated motion.

19. What is the SI unit of retardation?

Ans: The SI unit of retardation is also m/s² (same as acceleration).

20.

Fill in the following blanks with suitable words:

(a) Displacement is a vector quantity whereas distance is a scalar quantity.

(b) The physical quantity which gives both, the speed and direction of motion of a body is called its velocity.

(c) A motorcycle has a steady acceleration of 3 m/s². This means that every second, its velocity increases by 3 meters per second.

(d) Velocity is the rate of change of displacement. It is measured in meters per second.

(e) Acceleration is the rate of change of velocity. It is measured in meters per second squared.

Short Answer Type Questions

21. What type of motion, uniform or non-uniform, is exhibited by a freely falling body? Give reason for your answer.

Ans: Non-uniform motion. The freely falling body is subject to constant acceleration due to gravity, resulting in a change in velocity over time.

22. State whether speed is a scalar or a vector quantity. Give reason for your choice.

Ans: Scalar. Speed is a scalar quantity as it only indicates the magnitude of motion without specifying direction.

23. Bus X travels a distance of 360 km in 5 hours, whereas bus Y travels a distance of 476 km in 7 hours. Which bus travels faster?

Ans: Bus X. It has a higher average speed, calculated as distance divided by time (

Speed = \frac{Distance}{Time}

24. Arrange the following speeds in increasing order (keeping the least speed first):

(i) An athlete running with a speed of 10 m/s.

(ii) A bicycle moving with a speed of 200 m/min.

(iii) A scooter moving with a speed of 30 km/h.

Ans: To arrange the given speeds in increasing order, we need to convert them all to the same unit of measurement. Let's convert all speeds to meters per second (m/s).

Speed of the athlete: 10 m/s (already in m/s)
Speed of the bicycle: 200 m/min = 200 m / (60 min/s) = 3.33 m/s
Speed of the scooter: 30 km/h = 30 km/h * (1000 m/km) / (3600 s/h) = 8.33 m/s

Now, we have the speeds in m/s:

(i) Athlete: 10 m/s

(ii) Bicycle: 3.33 m/s

(iii) Scooter: 8.33 m/s

Arranging the speeds in increasing order:

(ii) Bicycle: 3.33 m/s

(iii) Scooter: 8.33 m/s

(i) Athlete: 10 m/s

Therefore, the speeds in increasing order are: 3.33 m/s, 8.33 m/s, 10 m/s.

25. (a) Write the formula for acceleration. Give the meaning of each symbol which occurs in it.

(b) A train starting from Railway Station attains a speed of 21 m/s in one minute. Find its acceleration.

Ans:

(a) Formula for acceleration:

Acceleration is the rate of change of velocity, which is a vector quantity. It is represented by the symbol 'a' and is defined as:

a = Δv/Δt

where:

a is the acceleration (in meters per second squared, m/s²)
Δv is the change in velocity (in meters per second, m/s)
Δt is the change in time (in seconds, s)

Meaning of symbols:

a: Acceleration (m/s²)
v: Velocity (m/s)
Δv: Change in velocity (m/s)
Δt: Change in time (s)

(b) Acceleration of a train:

Given:

Initial velocity (u) = 0 m/s (since the train starts from rest)
Final velocity (v) = 21 m/s
Time (t) = 1 minute = 60 seconds

Using the formula for acceleration:

a = (v - u) / t

Substituting the given values:

a = (21 m/s - 0 m/s) / 60 s

a = 0.35 m/s²

Therefore, the acceleration of the train is 0.35 meters per second squared.

26. (a) What term is used to denote the change of velocity with time?

(b) Give one word which means the same as ‘moving with a negative acceleration’.

(c) The displacement of a moving object in a given interval of time is zero. Would the distance travelled by the object also be zero? Give a reason for your answer.

Ans:

(a) The term used to denote the change of velocity with time is acceleration. Acceleration is a vector quantity, which means it has both magnitude and direction. The magnitude of acceleration is measured in meters per second squared (m/s²), while the direction of acceleration is the same as the direction of the change in velocity.

(b) One word that means the same as "moving with a negative acceleration" is decelerating. Deceleration is the process of slowing down, which means that the velocity of the object is decreasing. When an object decelerates, its acceleration is negative.

(c) If the displacement of a moving object in a given interval of time is zero, then the object has returned to its starting position. This means that the object has not traveled any distance, even though it may have moved back and forth during the interval. For example, if an object moves 10 meters to the right and then 10 meters back to the left, its displacement is zero, but the distance it has traveled is 20 meters.

27. A snail covers a distance of 100 meters in 50 hours. Calculate the average speed of the snail in km/h.

Ans: To calculate the average speed of the snail, we will use the formula:

average speed = total distance / total time

where:

total distance is the distance traveled by the object
total time is the time it takes for the object to travel the distance

We are given that the snail covers a distance of 100 meters in 50 hours. We need to convert the distance from meters to kilometers and the time from hours to seconds.

Distance in kilometers: 100 meters / 1000 meters/kilometer = 0.1 kilometers Time in seconds: 50 hours * 3600 seconds/hour = 180000 seconds

Now we can plug these values into the formula:

average speed = 0.1 kilometers / 180000 seconds

average speed = 0.000000555556 kilometers per second

To convert kilometers per second to kilometers per hour, we multiply by 3600:

average speed = 0.000000555556 kilometers per second * 3600 seconds per hour

average speed = 0.002 kilometers per hour

Therefore, the average speed of the snail is 0.002 kilometers per hour.

28. A tortoise moves a distance of 100 meters in 15 minutes. What is the average speed of the tortoise in km/h?

Ans: To calculate the average speed of the tortoise, we will use the formula:

average speed = total distance / total time

where:

total distance is the distance traveled by the object
total time is the time it takes for the object to travel the distance

We are given that the tortoise covers a distance of 100 meters in 15 minutes. We need to convert the distance from meters to kilometers and the time from minutes to hours.

Distance in kilometers: 100 meters / 1000 meters/kilometer = 0.1 kilometers Time in hours: 15 minutes * 1 hour/60 minutes = 0.25 hours

Now we can plug these values into the formula:

average speed = 0.1 kilometers / 0.25 hours

average speed = 0.4 kilometers per hour

Therefore, the average speed of the tortoise is 0.4 kilometers per hour.

29. If a sprinter runs a distance of 100 meters in 9.83 seconds, calculate his average speed in km/h.

Ans: Given:

Distance (d) = 100 meters
Time (t) = 9.83 seconds

Formula:

Average speed = distance / time

Calculation:

Average speed = 100 meters / 9.83 seconds ≈ 10.172 meters/second

Conversion to km/h:

1 meter/second = 3.6 km/h

Therefore, the sprinter's average speed in km/h is:

Average speed = 10.172 meters/second × 3.6 km/h ≈ 36.62 km/h

Answer:

The sprinter's average speed is 36.62 km/h.

30. A motorcyclist drives from place A to B with a uniform speed of 30 km/h and returns from place B to A with a uniform speed of 20 km/h. Find his average speed.

Ans: To find the average speed, we need to consider the total distance traveled and the total time taken. Let's assume the distance between place A and place B is 'd'.

The time taken to travel from A to B at 30 km/h is:

Time from A to B = Distance / Speed = d / 30 km/h

The time taken to travel from B to A at 20 km/h is:

Time from B to A = Distance / Speed = d / 20 km/h

The total time taken is the sum of the time taken from A to B and the time taken from B to A:

Total time = Time from A to B + Time from B to A = d/30 + d/20

The total distance traveled is twice the distance between place A and place B:

Total distance = 2d

Now, we can define the average speed as the total distance divided by the total time:

Average speed = Total distance / Total time = 2d / (d/30 + d/20)

To simplify the expression, find a common denominator for the fractions in the denominator:

Average speed = 2d / [(2d + 3d) / 60] = 2d / (5d / 60) = 2d * (60/5d) = 24 km/h

Therefore, the average speed of the motorcyclist is 24 km/h.

31. A motorcyclist starts from rest and reaches a speed of 6 m/s after traveling with uniform acceleration for 3 s. What is his acceleration?

Ans: I've been getting better at solving motion problems. Let's find the acceleration of the motorcyclist.

We are given that the motorcyclist starts from rest and reaches a speed of 6 m/s after traveling with uniform acceleration for 3 s. We need to find the acceleration.

We can use the following equation to solve for the acceleration:

a = v/t

where:

a is the acceleration (m/s²)
v is the final velocity (m/s)
t is the time (s)

Plugging in the given values, we get:

a = 6 m/s / 3 s

a = 2 m/s²

Therefore, the acceleration of the motorcyclist is 2 m/s².

32. An aircraft traveling at 600 km/h accelerates steadily at 10 km/h per second. Taking the speed of sound as 1100 km/h at the aircraft’s altitude, how long will it take to reach the ‘sound barrier’?

Ans: To solve this problem, we need to first determine the change in speed that the aircraft needs to achieve to reach the speed of sound. The speed of sound is 1100 km/h, and the aircraft is currently traveling at 600 km/h. Therefore, the aircraft needs to increase its speed by 500 km/h.

We know that the aircraft is accelerating at a rate of 10 km/h per second. Therefore, we can calculate the time it will take to reach the speed of sound by dividing the change in speed by the acceleration.

time = change in speed / acceleration

time = 500 km/h / 10 km/h per second

time = 50 seconds

Therefore, it will take the aircraft 50 seconds to reach the sound barrier.

33. If a bus traveling at 20 m/s is subjected to a steady deceleration of 5 m/s², how long will it take to come to rest?

Ans: To find the time it will take for the bus to come to rest, we can use the following equation:

v = u + at

where:

v is the final velocity (m/s)
u is the initial velocity (m/s)
a is the acceleration (m/s²)
t is the time (s)

We know that the initial velocity (u) is 20 m/s, the final velocity (v) is 0 m/s (because the bus comes to rest), and the acceleration (a) is -5 m/s² (because the bus is decelerating). Plugging in these values, we get:

0 = 20 - 5t

Solving for t, we get:

t = 4 s

Therefore, it will take the bus 4 seconds to come to rest.

Long Answer Type Questions

34. (a) What is the difference between ‘distance travelled’ by a body and its ‘displacement’? Explain with the help of a diagram.

(b) An ant travels a distance of 8 cm from P to Q and then moves a distance of 6 cm at right angles to PQ. Find its resultant displacement.

Ans:

(a) Difference between distance travelled and displacement

Distance travelled is the total length of the path covered by a moving object, regardless of its direction. It is a scalar quantity, meaning it has magnitude but no direction. Displacement, on the other hand, is the shortest distance between an object's initial and final positions. It is a vector quantity, meaning it has both magnitude and direction.

Diagram:

In the diagram, the object starts at point A and travels to point B along the path PQ. The distance travelled by the object is the length of path PQ, while the displacement is the straight line from A to B.

(b) Resultant displacement of an ant

The ant travels a distance of 8 cm from P to Q and then moves a distance of 6 cm at right angles to PQ. We can find the resultant displacement of the ant by using the Pythagorean theorem:

a² + b² = c²

where:

a is the distance from P to Q (8 cm)
b is the distance from Q to the final position (6 cm)
c is the resultant displacement

Plugging in the values, we get:

8² + 6² = c²

64 + 36 = c²

c² = 100

c = 10 cm

Therefore, the resultant displacement of the ant is 10 cm.

35. Define motion. What do you understand by the terms ‘uniform motion’ and ‘non-uniform motion’? Explain with examples.

Ans:

Definition of motion:

Motion is the change in position of an object over time. It is a fundamental concept in physics that describes how objects move and interact with their surroundings. Motion can be described by various parameters, including velocity, acceleration, and displacement.

Uniform motion:

Uniform motion is a type of motion in which an object travels at a constant speed in a straight line. This means that the object's velocity remains unchanged throughout its motion. Examples of uniform motion include:

A car moving at a constant speed on a straight highway
A ball rolling smoothly on a flat surface

Non-uniform motion:

Non-uniform motion is a type of motion in which an object's speed or direction is constantly changing. This means that the object's velocity is not constant. Examples of non-uniform motion include:

A car accelerating or decelerating
A ball thrown into the air and falling back to the ground
A planet orbiting the Sun in an elliptical path

36. (a) Define speed. What is the SI unit of speed?

(b) What is meant by (i) average speed, and (ii) uniform speed?

Ans:

a. Definition of speed and its SI unit

Speed is a scalar quantity that describes how fast an object is moving. It is defined as the rate of change of displacement over time. The SI unit of speed is meters per second (m/s).

Here is the formula for speed:

speed = Δdisplacement / Δtime

where:

Δdisplacement is the change in displacement
Δtime is the change in time

b. Average speed and uniform speed

i. Average speed

Average speed is the total distance traveled divided by the total time taken. It is a scalar quantity that does not take into account the direction of motion.

Here is the formula for average speed:

average speed = total distance / total time

For example, if a car travels 100 kilometers in 2 hours, its average speed is 50 kilometers per hour (km/h).

ii. Uniform speed

Uniform speed is a type of motion in which an object travels at a constant speed in a straight line. This means that the object's velocity remains unchanged throughout its motion.

For example, a car moving at a constant speed of 60 km/h on a straight highway is traveling at uniform speed.

I hope this helps!

37. (a) Define velocity. What is the SI unit of velocity?

(b) What is the difference between speed and velocity?

Ans: (a) Velocity: Velocity is the rate of change of displacement with respect to time. The SI unit of velocity is meters per second (m/s).

(b) Difference: Speed is a scalar quantity, while velocity is a vector quantity as it includes direction.

38. (a) What is meant by the term ‘acceleration’? State the SI unit of acceleration.

(b) Define the term ‘uniform acceleration.’ Give one example of a uniformly accelerated motion.

Ans:

a. Definition and SI unit of acceleration

Acceleration is the rate of change of velocity, which is a vector quantity. It is defined as the change in velocity divided by the change in time. The SI unit of acceleration is meters per second squared (m/s²).

Here is the formula for acceleration:

acceleration = Δv/Δt

where:

acceleration is the rate of change of velocity (m/s²)
Δv is the change in velocity (m/s)
Δt is the change in time (s)

b. Definition of uniform acceleration and example

Uniform acceleration is a type of motion in which an object's acceleration is constant. This means that the object's velocity is changing at a constant rate. One example of a uniformly accelerated motion is the motion of a freely falling object near the Earth's surface. The acceleration due to gravity near the Earth's surface is approximately 9.8 m/s², so an object falling freely near the Earth's surface will accelerate at a rate of 9.8 m/s² until it hits the ground.

39. The distance between Delhi and Agra is 200 km. A train travels the first 100 km at a speed of 50 km/h. How fast must the train travel the next 100 km, so as to average 70 km/h for the whole journey?

Ans:

To find the speed the train must travel for the next 100 km, we can use the concept of average speed. Average speed is the total distance traveled divided by the total time taken.

Let's denote the time taken to travel the first 100 km as t1 and the time taken to travel the next 100 km as t2. We are given that the average speed for the whole journey is 70 km/h. This means that the total time taken for the entire journey (T) is:

T = total distance / average speed

T = 200 km / 70 km/h

T = 2.857 hours

We are also given that the train travels the first 100 km at a speed of 50 km/h. This means that the time taken to travel the first 100 km (t1) is:

t1 = distance / speed

t1 = 100 km / 50 km/h

t1 = 2 hours

Now we can calculate the time taken to travel the next 100 km (t2) using the formula for average speed:

average speed = (total distance / total time)

70 km/h = (200 km / (t1 + t2))

Multiplying both sides by (t1 + t2), we get:

70(t1 + t2) = 200

Solving for t2, we get:

t2 = (200 - 70t1) / 70

Substituting the value of t1 from the previous calculation, we get:

t2 = (200 - 70 * 2) / 70

t2 = 85.71 / 70

t2 ≈ 1.22 hours

Now we can calculate the speed for the next 100 km (v2) using the formula:

speed = distance / time

v2 = 100 km / 1.22 hours

v2 ≈ 81.97 km/h

Therefore, the train must travel the next 100 km at a speed of approximately 81.97 km/h to maintain an average speed of 70 km/h for the whole journey.

40. A train travels the first 15 km at a uniform speed of 30 km/h; the next 75 km at a uniform speed of 50 km/h; and the last 10 km at a uniform speed of 20 km/h. Calculate the average speed for the entire train journey.

Ans:

To calculate the average speed, we need to find the total distance traveled and the total time taken.

The total distance traveled is 15 km + 75 km + 10 km = 100 km.

To find the total time taken, we can use the formula:

Time = Distance / Speed

For the first part of the journey, the time taken is 15 km / 30 km/h = 0.5 hours.

For the second part of the journey, the time taken is 75 km / 50 km/h = 1.5 hours.

For the third part of the journey, the time taken is 10 km / 20 km/h = 0.5 hours.

The total time taken is 0.5 hours + 1.5 hours + 0.5 hours = 2.5 hours.

Now we can calculate the average speed using the formula:

Average speed = Total distance / Total time

Average speed = 100 km / 2.5 hours = 40 km/h

Therefore, the average speed for the entire train journey is 40 km/h

41. A car is moving along a straight road at a steady speed. It travels 150 m in 5 seconds:

(a) What is its average speed?

(b) How far does it travel in 1 second?

(c) How far does it travel in 6 seconds?

(d) How long does it take to travel 240 m?

Ans:

(a) Average speed

Average speed is the total distance traveled divided by the total time taken. In this case, the car travels 150 meters in 5 seconds. Therefore, its average speed is:

Average speed = Distance / Time = 150 meters / 5 seconds = 30 meters per second (m/s)

(b) Distance traveled in 1 second

If the car travels at a steady speed of 30 m/s, then it travels 30 meters in every second. Therefore, the distance it travels in 1 second is:

Distance = Speed × Time = 30 m/s × 1 s = 30 meters

If the car travels at a steady speed of 30 m/s, then it travels 30 meters in every second. Therefore, the distance it travels in 6 seconds is:

Distance = Speed × Time = 30 m/s × 6 s = 180 meters

(d) Time taken to travel 240 meters

To find the time it takes the car to travel 240 meters, we can use the formula:

Time = Distance / Speed

Substituting the values, we get:

Time = 240 meters / 30 m/s = 8 seconds

Therefore, it takes the car 8 seconds to travel 240 meters.

Multiple Choice Questions (MCQs)

42. A particle is moving in a circular path of radius

$�$ . The displacement after half a circle would be :

(a) 0 (b) $�_{�}$ (c) $2 �$ (d)

Ans: (c) $�_{�}$

A particle moving in a circular motion will not have any displacement. A particle's displacement is the change in its position. In circular motion, the particle's position is constantly changing, but its displacement remains zero. This is because the particle returns to the same point after completing one full rotation.

The distance covered by the particle after half a circle would be 2r. The distance covered in a circular motion is the length of the path followed by the particle. After half a circle, the particle will have covered the length of the semi-circle. The circumference of a circle is given by 2πr, so the distance covered after half a circle is half the circumference, or 2r.

43. The numerical ratio of displacement to distance for a moving object is :

(a) always less than 1 (b) equal to 1 or more than 1

(c) always more than 1 (d) equal to 1 or less than 1

Ans: (d) equal to 1 or less than 1

Displacement is the shortest distance between an object's initial and final positions, while distance is the total length of the path traveled by the object. Since displacement is always the shortest path between two points, it can never be greater than the distance traveled. Therefore, the ratio of displacement to distance is always equal to 1 or less than 1.

For example, consider an object that moves from point A to point B in a straight line. The distance traveled is the length of the line segment AB, while the displacement is also the length of AB. In this case, the ratio of displacement to distance is 1.

However, if the object does not move in a straight line, the distance traveled will be greater than the displacement. For example, consider an object that moves from point A to point B in a curved path. The distance traveled is the length of the curved path, while the displacement is the length of the straight line segment AB. In this case, the ratio of displacement to distance is less than 1.

Therefore, the correct answer is (d) equal to 1 or less than 1.

44. A boy is sitting on a merry-go-round which is moving with a constant speed of $10 m/s$ . This means that the boy is :

(a) at rest (b) moving with no acceleration

(c) in accelerated motion (d) moving with uniform velocity

Ans: (c) in accelerated motion

Since the boy is moving in a circular motion, his velocity is constantly changing direction even though his speed remains constant. Therefore, the boy is in accelerated motion.

Acceleration is the rate of change of velocity, and it is not just about the magnitude of the velocity but also the direction. Since the boy's velocity is changing direction, he is experiencing acceleration.

The other options are incorrect because:

At rest: This means the boy is not moving at all.
Moving with no acceleration: This means the boy's velocity is constant in both magnitude and direction.
Moving with uniform velocity: This means the boy's magnitude of velocity is constant, but the direction is not necessarily constant.

Therefore, the only correct answer is in accelerated motion.

45. In which of the following cases of motion, the distance moved and the magnitude of displacement are equal ?

(a) if the car is moving on a straight road (b) if the car is moving on a circular road

(c) if the pendulum is moving to and fro (d) if a planet is moving around the sun

Ans: (a) if the car is moving on a straight road

When a car is moving on a straight road, the distance moved and the magnitude of displacement are equal. This is because the direction of motion remains constant, and the car's position changes along a straight line. Therefore, the distance traveled and the displacement coincide, resulting in equal values.

Options (b), (c), and (d) represent cases where the distance moved and the magnitude of displacement are not equal. In circular motion, the car's path is curved, and its position changes direction. Therefore, the distance traveled along the curved path is greater than the straight-line displacement between the initial and final positions.

Similarly, in the case of a pendulum swinging back and forth, the distance traveled along the curved path is greater than the straight-line displacement between the extreme positions. For a planet orbiting the Sun, the path is an elliptical orbit, and the distance traveled along the entire orbit is greater than the straight-line displacement between the planet's starting and ending points.

Therefore, only in the case of a car moving on a straight road are the distance moved and the magnitude of displacement equal.

46. The speed of a moving object is determined to be $0.06 m/s$ . This speed is equal to :

(a) $2.16 km/h$ (b) $1.08 km/h$ (c) $0.216 km/h$ (b) $0.0216 km/h$

Ans: (c) $0.216 km/h$

To convert the speed from meters per second (m/s) to kilometers per hour (km/h), we can use the following conversion factor:

1 km/h = 1000 m/3600 s

Therefore, we can convert 0.06 m/s to km/h using the following formula:

0.06 m/s × (1 km/h) / (1000 m/3600 s) = 0.216 km/h

Therefore, the speed of the moving object is equal to 0.216 km/h. The other options are incorrect because they represent either a higher speed (a) or a lower speed (b, d).

47. A freely falling object travels $4.9 m$ in the 1st second, $14.7 m$ in the 2nd second, $24.5 m$ in the 3rd second, and so on. This data shows that the motion of a freely falling object is a case of :

(a) uniform motion (b) uniform acceleration

(c) no acceleration (d) uniform velocity

Ans: (b) uniform acceleration

A freely falling object experiences uniform acceleration due to the gravitational pull of the Earth. This means that the object's velocity increases at a constant rate. As a result, the object's displacement increases at an increasing rate.

The data provided shows that the object's displacement increases by 9.8 m each second. This is consistent with the concept of uniform acceleration, where the velocity of the object increases by a constant value each second.

Options (a), (c), and (d) are incorrect because they do not accurately describe the motion of a freely falling object. Uniform motion implies constant speed and constant direction, which is not the case for a freely falling object. No acceleration implies that the object's velocity is not changing, which is also not the case for a freely falling object. Uniform velocity implies that the object's speed and direction are both constant, which is not the case for a freely falling object.

Therefore, the only option that accurately describes the motion of a freely falling object is uniform acceleration.

48. When a car runs on a circular track with a uniform speed, its velocity is said to be changing. This is because :

(a) the car has a uniform acceleration

(b) the direction of the car varies continuously

(c) the car travels unequal distances in equal time intervals

(d) the car travels equal distances in unequal time intervals

Ans: (b) the direction of the car varies continuously

When a car runs on a circular track with a uniform speed, its velocity is said to be changing because the direction of the car varies continuously. Even though the speed of the car remains constant, the direction of its motion is constantly changing as it travels along the curved path.

Option (a) is incorrect because the car does not have a uniform acceleration. The acceleration of the car is directed towards the center of the circle, and it is not constant.

Option (c) is incorrect. The car travels equal distances in equal time intervals along a circular track. This is because the speed of the car is constant.

Option (d) is incorrect. The car travels unequal distances in equal time intervals along a circular track. This is because the circumference of the circle is not constant.

Therefore, the only option that correctly explains why a car's velocity changes when it runs on a circular track with a uniform speed is because the direction of the car varies continuously.

49. Which of the following statements is correct regarding velocity and speed of a moving body ?

(a) velocity of a moving body is always higher than its speed

(b) speed of a moving body is always higher than its velocity

(c) speed of a moving body is its velocity in a given direction

(d) velocity of a moving body is its speed in a given direction

Ans: (d) velocity of a moving body is its speed in a given direction

Speed is a scalar quantity that describes the magnitude of an object's motion, while velocity is a vector quantity that describes both the magnitude and direction of an object's motion. Therefore, velocity is more specific than speed, as it includes information about the direction of motion.

Option (a) is incorrect because velocity of a moving body is not always higher than its speed. In fact, velocity can be equal to speed if the object is moving in a straight line.

Option (b) is incorrect because speed of a moving body is not always higher than its velocity. In fact, velocity is always equal to or less than speed.

Option (c) is incorrect because speed of a moving body is not its velocity in any given direction. Speed is simply the magnitude of an object's motion, regardless of its direction.

Therefore, the only correct statement is that velocity of a moving body is its speed in a given direction. This is because velocity includes information about both the magnitude and direction of an object's motion.

50. Which of the following can sometimes be ‘zero’ for a moving body ?

(i) average velocity (ii) distance travelled (iii) average speed (iv) displacement

(a) only (i) (b) (i) and (ii) (c) (i) and (iv) (d) only (iv)

Ans: (c) (i) and (iv).

Distance traveled can never be zero for a moving body. The distance traveled is the total length of the path covered by the body, and it is always a positive quantity.
Average speed can also never be zero for a moving body. Average speed is the total distance traveled divided by the total time taken, and it is always a positive quantity.
Displacement can be zero for a moving body. Displacement is the change in position of the body, and it is a vector quantity. If the body returns to its starting position, then its displacement is zero. For example, if a body moves in a circular path, then its displacement after one full revolution is zero.
Average velocity can also be zero for a moving body. Average velocity is the total displacement divided by the total time taken, and it is a vector quantity. If the body's displacement is zero, then its average velocity is zero. For example, if a body moves back and forth in a straight line, then its average velocity over a period of time that includes both forward and backward motion can be zero.

Therefore, the only options that include both average velocity and displacement are (i) and (iv), and (c) is the correct answer.

51. When a car driver traveling at a speed of $10 m/s$ applies brakes and brings the car to rest in $20 s$ , then retardation will be :

(a) $+ 2 {m/s}^{2}$ (b) $- 2 {m/s}^{2}$ (c) $- 0.5 {m/s}^{2}$ (d) $+ 0.5 {m/s}^{2}$

Ans: (b) $- 2 {m/s}^{2}$

Retardation, also known as deceleration, is the rate of change of velocity in the opposite direction of motion. In this case, the car is slowing down, so the retardation is negative.
We can use the formula:
retardation = (final velocity - initial velocity) / time
In this case, the initial velocity is 10 m/s and the final velocity is 0 m/s (since the car comes to rest). The time is 20 s. Plugging these values into the formula, we get:
retardation = (0 m/s - 10 m/s) / 20 s = −0.5 m/s²
Therefore, the retardation is −0.5 m/s². This means that the car's velocity is decreasing at a rate of 0.5 meters per second every second.
52.Which of the following could not be a unit of speed ?

(a) $km/h$ (b) $s/m$ (c) $m/s$ (d) ${mm s}^{- 1}$

Ans: (b) $s/m$

The units of speed represent the distance traveled per unit of time. Out of the given options, s/m represents seconds per meter, which is the inverse of speed. Therefore, option (b) s/m cannot be a unit of speed.

The remaining options, (a) km/h, (c) m/s, and (d) mm s−1, all represent distance per unit of time and are valid units of speed.

Hence, the incorrect answer is (b) s/m.

53.One of the following is not a vector quantity. This one is :

(a) displacement (b) speed (c) acceleration (d) velocity

Ans: (b) speed

Speed is a scalar quantity, while displacement, acceleration, and velocity are vector quantities. Scalar quantities are defined by only one value, while vector quantities are defined by both magnitude and direction.

Speed is the rate of change of distance, and it is only defined by its magnitude. Displacement is the change in position, and it is defined by both magnitude and direction. Acceleration is the rate of change of velocity, and it is defined by both magnitude and direction. Velocity is the combination of speed and direction, and it is therefore a vector quantity.

Therefore, the only option that is not a vector quantity is speed.

54. Which of the following could not be a unit of acceleration ?

(a) ${km/s}^{2}$ (b) ${cm s}^{- 2}$ (c) $km/s$ (d) ${m/s}^{2}$

Ans: (c) $km/s$

Acceleration is the rate of change of velocity, and the SI unit of acceleration is meters per second squared (m/s²).

Out of the given options, km/s represents kilometers per second, which is a unit of velocity. Therefore, option (c) km/s cannot be a unit of acceleration.

The remaining options, (a) km/s², (b) cm s⁻², and (d) m/s², all represent the rate of change of displacement per unit of time and are valid units of acceleration.

Hence, the incorrect answer is (c) km/s.

Questions Based on High Order Thinking Skills (HOTS)

55. A body is moving along a circular path of radius R. What will be the distance travelled and displacement of the body when it completes half a revolution?

Ans: The distance traveled by a body when it completes half a revolution along a circular path is equal to the circumference of a semicircle, which is given by:

distance = 1/2 * 2πR = πR

where R is the radius of the circular path.

The displacement of the body when it completes half a revolution is equal to the diameter of the circle, which is given by:

displacement = 2R

Therefore, the distance traveled by the body is πR and the displacement of the body is 2R.

56. If on a round trip you travel 6 km and then arrive back home:

(a) What distance have you travelled?

(b) What is your final displacement?

Ans:

(a) The distance traveled is the total length of the journey, which is 6 km.

(b) The displacement is the change in position from the starting point to the ending point. In this case, you have traveled 6 km to a destination and then returned home, which means you have ended up back at your starting point. Therefore, your displacement is 0 km.

57. A body travels a distance of 3 km towards East, then 4 km towards North and finally 9 km towards East.

(i) What is the total distance travelled?

(ii) What is the resultant displacement?

Ans:


To solve this problem, we can use vector addition to find the total displacement.
Let's denote the distances traveled in the East direction as  $�$ , in the North direction as  $�$ , and the total displacement as  $�$ .
Given:
 $�_{1} = 3 km$  (eastward),
 $�_{1} = 0 km$  (no northward movement),
 $�_{2} = 0 km$  (no eastward movement),
 $�_{2} = 4 km$  (northward),
 $�_{3} = 9 km$  (eastward),
 $�_{3} = 0 km$  (no northward movement).
(i) Total distance traveled ( $�_{total}$ ) is the sum of the magnitudes of the individual displacements:
 $�_{total} = �_{1} + �_{2} + �_{3} = 3 km + 4 km + 9 km$ 
 $�_{total} = 16 km$ 
So, the total distance traveled is  $16 km$ .
(ii) Resultant displacement ( $�$ ) is the vector sum of the individual displacements. We can use the Pythagorean theorem for this:
 $� = \sqrt{(�_{1} + �_{3})^{2} + (�_{2})^{2}}$ 
 $� = \sqrt{(3 km + 9 km)^{2} + (4 km)^{2}}$ 
 $� = \sqrt{(12 km)^{2} + (4 km)^{2}}$ 
 $� = \sqrt{144 {km}^{2} + 16 {km}^{2}}$ 
 $� = \sqrt{160 {km}^{2}}$ 
 $� = 4 \sqrt{10} km$ 
= 12.65 km

Therefore, the total distance traveled is 16 km and the resultant displacement is 12.65 km.

58. A boy walks from his classroom to the bookshop along a straight corridor towards North. He covers a distance of 20 m in 25 seconds to reach the bookshop. After buying a book, he travels the same distance in the same time to reach back in the classroom. Find (a) average speed, and (b) average velocity, of the boy.

Ans:

(a) Average speed is defined as the total distance traveled divided by the total time taken. In this case, the boy travels a total distance of 20 m (to the bookshop and back) in a total time of 25 seconds (to the bookshop and back). Therefore, the average speed is:

average speed = (20 m) / (25 s) = 0.8 m/s

(b) Average velocity is defined as the displacement divided by the time taken. In this case, the displacement is the change in position of the boy. Since the boy starts and ends at the same classroom, his displacement is 0 m. Therefore, the average velocity is:

average velocity = (0 m) / (25 s) = 0 m/s

So, the average speed of the boy is 0.8 m/s, while his average velocity is 0 m/s.

59. A car travels 100 km at a speed of 60 km/h and returns with a speed of 40 km/h. Calculate the average speed for the whole journey.

Ans: To determine the average speed of the car for the whole journey, we need to consider both the distance traveled and the time taken for each leg of the trip.

Outward journey: Distance = 100 km Speed = 60 km/h

Time taken = Distance/Speed = 100 km / 60 km/h = 1.67 hours

Return journey: Distance = 100 km Speed = 40 km/h

Time taken = Distance/Speed = 100 km / 40 km/h = 2.5 hours

Total distance: 100 km (outward) + 100 km (return) = 200 km

Total time: 1.67 hours (outward) + 2.5 hours (return) = 4.17 hours

Now, we can calculate the average speed for the whole journey using the formula:

Average speed = Total distance / Total time

Average speed = 200 km / 4.17 hours = 47.96 km/h

Therefore, the average speed of the car for the whole journey is approximately 48 km/h.

60. A ball hits a wall horizontally at 6.0 m/s. It rebounds horizontally at 4.4 m/s. The ball is in contact with the wall for 0.040 s. What is the acceleration of the ball?

Ans: Given:

Initial velocity ( $�_{initial}$ ) = $6.0 m/s$ (to the right),
Final velocity ( $�_{final}$ ) = $- 4.4 m/s$ (to the left),
Time ( $Δ �$ ) = $0.040 s$ .

The change in velocity ( $Δ �$ ) is calculated as:

$Δ � = �_{final} - �_{initial}$

$Δ � = (- 4.4 m/s) - (6.0 m/s)$

$Δ � = - 10.4 m/s$

Now, we can use the formula for acceleration:

$� = \frac{Δ �}{Δ �}$

$� = \frac{- 10.4 m/s}{0.040 s}$

$� = - 260 {m/s}^{2}$

Therefore, the acceleration of the ball is -260 m/s².

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