The NCERT solutions provided here align with the NCERT (National Council of Educational Research and Training) and JKBOSE (Jammu and Kashmir Board of School Education) curricula for Class 9 Science Chapter 1 Motion. Both boards follow a similar syllabus for this chapter, and the answers provided will help students prepare for their exams by understanding and solving problems related to motion effectively.

NCERT Solutions of Motion Class 9 Science Questions and Answers:

1. An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.

Answer: Yes, an object can have zero displacement if it returns to its initial position. For example, if a person walks around a circular track and returns to the starting point, the distance traveled is the circumference of the circle, but the displacement is zero.

2. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?

Answer: The total time is 2 minutes 20 seconds, which is 140 seconds. Since the field is a square with a perimeter of 40 m, the farmer completes one round in 40 seconds. In 140 seconds, the farmer completes 3.5 rounds (140 / 40 = 3.5). Therefore, the magnitude of the displacement is the length of the diagonal of the square field. The diagonal is calculated as √(10² + 10²) = √200 = 10√2 m ≈ 14.14 m.

3. Which of the following is true for displacement?

Its magnitude is greater than the distance travelled by the object.
Answer: False. The magnitude of displacement is never greater than the distance traveled; it can be equal to or less than the distance.

4. Distinguish between speed and velocity.

Answer:

Speed is a scalar quantity that refers to how fast an object is moving, irrespective of its direction.
Velocity is a vector quantity that refers to the rate at which an object changes its position, and it includes both speed and direction.

5. Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?

Answer: The magnitude of average velocity is equal to its average speed when the object moves in a straight line in a single direction without changing direction.

6. What does the odometer of an automobile measure?

Answer: The odometer of an automobile measures the total distance traveled by the vehicle.

7. What does the path of an object look like when it is in uniform motion?

Answer: When an object is in uniform motion, its path is a straight line.

8. During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, 3 × 10⁸ m/s.

Answer: The time taken for the signal to travel is 5 minutes = 300 seconds. Distance = speed × time = 3 × 10⁸ m/s × 300 s = 9 × 10¹⁰ meters.

9. When will you say a body is in (i) uniform acceleration? (ii) nonuniform acceleration?

Answer:

(i) A body is in uniform acceleration when it changes its velocity by equal amounts in equal intervals of time.
(ii) A body is in nonuniform acceleration when it changes its velocity by unequal amounts in equal intervals of time.

10. A bus decreases its speed from 80 km/h to 60 km/h in 5 seconds. Find the acceleration of the bus.

Answer: The initial speed (u) is 80 km/h (22.22 m/s) and the final speed (v) is 60 km/h (16.67 m/s). The time (t) is 5 seconds.

Acceleration (a) = (v – u) / t = (16.67 – 22.22) / 5 = -1.11 m/s².

11. A train starting from a railway station and moving with uniform acceleration attains a speed of 40 km/h in 10 minutes. Find its acceleration.

Answer: The initial speed (u) is 0, the final speed (v) is 40 km/h (11.11 m/s), and the time (t) is 10 minutes (600 seconds).

Acceleration (a) = (v – u) / t = (11.11 – 0) / 600 = 0.0185 m/s².

12. What is the nature of the distance-time graphs for uniform and non-uniform motion of an object?

Answer:

For uniform motion, the distance-time graph is a straight line.
For non-uniform motion, the distance-time graph is a curved line.

13. What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?

Answer: If the distance-time graph is a straight line parallel to the time axis, the object is at rest and not moving.

14. What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis?

Answer: If the speed-time graph is a straight line parallel to the time axis, the object is moving with constant speed.

15. What is the quantity which is measured by the area occupied below the velocity-time graph?

Answer: The area occupied below the velocity-time graph represents the displacement of the object.

16. A bus starting from rest moves with a uniform acceleration of 0.1 m/s² for 2 minutes. Find (a) the speed acquired, (b) the distance travelled.

Answer:

(a) Speed acquired (v) = u + at = 0 + 0.1 × 120 = 12 m/s.
(b) Distance travelled (s) = ut + 0.5at² = 0 + 0.5 × 0.1 × 120² = 720 meters.

17. A train is travelling at a speed of 90 km/h. Brakes are applied so as to produce a uniform acceleration of -0.5 m/s². Find how far the train will go before it is brought to rest.

Answer: Initial speed (u) = 90 km/h (25 m/s), final speed (v) = 0, acceleration (a) = -0.5 m/s².

Using v2=u2+2asv² = u² + 2asv2=u2+2as: 0 = 25² + 2(-0.5)s 0 = 625 – s s = 625 / 1 s = 312.5 meters.

18. A trolley, while going down an inclined plane, has an acceleration of 2 cm/s². What will be its velocity 3 s after the start?

Answer: Initial velocity (u) = 0, acceleration (a) = 2 cm/s² (0.02 m/s²), time (t) = 3 s. Velocity (v) = u + at = 0 + 0.02 × 3 = 0.06 m/s.

19. A racing car has a uniform acceleration of 4 m/s². What distance will it cover in 10 s after start?

Answer: Initial velocity (u) = 0, acceleration (a) = 4 m/s², time (t) = 10 s. Distance (s) = ut + 0.5at² = 0 + 0.5 × 4 × 10² = 200 meters.

20. A stone is thrown in a vertically upward direction with a velocity of 5 m/s. If the acceleration of the stone during its motion is 10 m/s² in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

Answer:

Final velocity (v) = 0, initial velocity (u) = 5 m/s, acceleration (a) = -10 m/s². Using v2=u2+2asv² = u² + 2asv2=u2+2as: 0 = 5² + 2(-10)s 0 = 25 – 20s 20s = 25 s = 1.25 meters.
Time to reach the highest point (t) = (v – u) / a = (0 – 5) / -10 = 0.5 seconds.

21. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?

Answer:

Total time is 2 minutes 20 seconds, which is 140 seconds. The athlete completes one round in 40 seconds, so in 140 seconds, the athlete completes 3.5 rounds.
Distance covered = 3.5 × π × 200 = 2200 meters.
Displacement is the diameter of the track since the athlete ends up halfway around the track from the start. Displacement = 200 meters.

22. Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C?

Answer:

(a) From A to B:
- Distance = 300 m, time = 2.5 minutes = 150 seconds.
- Average speed = Distance / Time = 300 / 150 = 2 m/s.
- Displacement = 300 m, Average velocity = Displacement / Time = 300 / 150 = 2 m/s.
(b) From A to C:
- Distance = 300 + 100 = 400 m, time = 2.5 + 1 = 3.5 minutes = 210 seconds.
- Average speed = Distance / Time = 400 / 210 ≈ 1.9 m/s.
- Displacement = 300 – 100 = 200 m, Average velocity = Displacement / Time = 200 / 210 ≈ 0.95 m/s.

23. Abdul, while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 30 km/h. What is the average speed for Abdul’s trip?

Answer: Let the distance be D km.

Time for the trip to school = D / 20 hours.
Time for the return trip = D / 30 hours.
Total distance = 2D km.
Total time = (D / 20) + (D / 30) = (3D + 2D) / 60 = 5D / 60 = D / 12 hours.
Average speed = Total distance / Total time = 2D / (D / 12) = 24 km/h.

24. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s² for 8.0 s. How far does the boat travel during this time?

Answer: Initial velocity (u) = 0, acceleration (a) = 3 m/s², time (t) = 8 s. Distance (s) = ut + 0.5at² = 0 + 0.5 × 3 × 8² = 96 meters.

25. A driver of a car travelling at 52 km/h applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 seconds. Another driver going at 3 km/h in another car applies his brakes slowly and stops in 10 seconds. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?

Answer:

Car 1: Initial speed = 52 km/h (14.44 m/s), time = 5 s. Final speed = 0. Acceleration = (0 – 14.44) / 5 = -2.89 m/s². Distance = 0.5 × (14.44 + 0) × 5 = 36.1 meters.
Car 2: Initial speed = 3 km/h (0.83 m/s), time = 10 s. Final speed = 0. Acceleration = (0 – 0.83) / 10 = -0.083 m/s². Distance = 0.5 × (0.83 + 0) × 10 = 4.15 meters.
Car 1 travels farther after the brakes were applied.

Exercise

1. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?

Answer:

Distance covered in one round = Circumference of the circle = π × diameter = 3.14 × 200 = 628 m.
Time for one round = 40 s.
Total time = 2 minutes 20 seconds = 140 seconds.
Number of rounds completed in 140 seconds = 140 / 40 = 3.5 rounds.
Distance covered = 3.5 × 628 = 2198 meters.
Displacement = 0 (since the athlete returns to the starting point after completing full rounds).

2. Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C?

Answer: (a) From A to B:

Distance = 300 m, time = 2.5 minutes = 150 seconds.
Average speed = Distance / Time = 300 / 150 = 2 m/s.
Displacement = 300 m, Average velocity = Displacement / Time = 300 / 150 = 2 m/s.

(b) From A to C:

Distance = 300 + 100 = 400 m, time = 2.5 + 1 = 3.5 minutes = 210 seconds.
Average speed = Distance / Time = 400 / 210 ≈ 1.9 m/s.
Displacement = 300 – 100 = 200 m, Average velocity = Displacement / Time = 200 / 210 ≈ 0.95 m/s.

3. Abdul, while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 30 km/h. What is the average speed for Abdul’s trip?

Answer: Let the distance be D km.

Time for the trip to school = D / 20 hours.
Time for the return trip = D / 30 hours.
Total distance = 2D km.
Total time = (D / 20) + (D / 30) = (3D + 2D) / 60 = 5D / 60 = D / 12 hours.
Average speed = Total distance / Total time = 2D / (D / 12) = 24 km/h.

4. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s² for 8.0 s. How far does the boat travel during this time?

Answer: Initial velocity (u) = 0, acceleration (a) = 3 m/s², time (t) = 8 s. Distance (s) = ut + 0.5at² = 0 + 0.5 × 3 × 8² = 96 meters.

5. A driver of a car travelling at 52 km/h applies the brakes and accelerates uniformly in the opposite direction. The car stops in 5 seconds. Another driver going at 3 km/h in another car applies his brakes slowly and stops in 10 seconds. On the same graph paper, plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?

Answer:

Car 1: Initial speed = 52 km/h (14.44 m/s), time = 5 s. Final speed = 0. Acceleration = (0 – 14.44) / 5 = -2.89 m/s². Distance = 0.5 × (14.44 + 0) × 5 = 36.1 meters.
Car 2: Initial speed = 3 km/h (0.83 m/s), time = 10 s. Final speed = 0. Acceleration = (0 – 0.83) / 10 = -0.083 m/s². Distance = 0.5 × (0.83 + 0) × 10 = 4.15 meters.
Car 1 travels farther after the brakes were applied.

6. Fig 8.11 shows the distance-time graph of three objects A, B, and C. Study the graph and answer the following questions:

(a) Which of the three is travelling the fastest?

Answer: Object B is travelling the fastest as it has the steepest slope on the distance-time graph.

(b) Are all three ever at the same point on the road?

Answer: No, all three objects are never at the same point on the road.

Answer: When B passes A at around 1.1 hours, C has travelled approximately 9 km.

(d) How far has B travelled by the time it passes C?

Answer: B passes C at around 1.4 hours and has travelled approximately 11 km.

7. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m/s², with what velocity will it strike the ground? After what time will it strike the ground?

Answer:

Initial velocity (u) = 0 m/s, acceleration (a) = 10 m/s², distance (s) = 20 m.
Using the equation v2=u2+2asv^2 = u^2 + 2asv2=u2+2as: v2=0+2×10×20v^2 = 0 + 2 \times 10 \times 20v2=0+2×10×20 v2=400v^2 = 400v2=400 v=20v = 20v=20 m/s.
Using the equation v=u+atv = u + atv=u+at: 20=0+10t20 = 0 + 10t20=0+10t t=2t = 2t=2 seconds.
The ball will strike the ground with a velocity of 20 m/s after 2 seconds.

8. The speed-time graph for a car is shown as Fig. 8.12.

(a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance travelled by the car during the period.

Answer:

The area under the speed-time graph represents the distance travelled.
From the graph, the car starts from 0 m/s and reaches 4 m/s in 4 seconds.
The area under the graph (a triangle) = 0.5 × base × height = 0.5 × 4 s × 4 m/s = 8 m.
The car travels 8 meters in the first 4 seconds.

(b) Which part of the graph represents uniform motion of the car?

Answer:

The part of the graph where the speed remains constant (horizontal line) represents the uniform motion of the car.

9. State which of the following situations are possible and give an example for each of these:

(a) An object with a constant acceleration but with zero velocity.

Answer:

Possible. Example: An object thrown vertically upward at its highest point has zero velocity but is accelerating downwards due to gravity.

(b) An object moving with an acceleration but with uniform speed.

Answer:

Not possible. If an object is accelerating, its speed cannot remain uniform.

Answer:

Possible. Example: An object moving in a circular path at constant speed has an acceleration directed towards the center of the circle (centripetal acceleration), which is perpendicular to the direction of motion.

10. An artificial satellite is moving in a circular orbit of radius 42,250 km. Calculate its speed if it takes 24 hours to revolve around the earth.

Answer:

Radius (r) = 42,250 km, time period (T) = 24 hours.
Circumference of the orbit = 2πr = 2 × 3.14 × 42,250 = 265,500 km.
Speed (v) = Distance / Time = 265,500 km / 24 hours = 11,062.5 km/h.

NCERT Solutions of Motion Class 9 Science Questions and Answers:

1. An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.

2. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds from his initial position?

3. Which of the following is true for displacement?

4. Distinguish between speed and velocity.

5. Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?

6. What does the odometer of an automobile measure?

7. What does the path of an object look like when it is in uniform motion?

8. During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, 3 × 10⁸ m/s.

9. When will you say a body is in (i) uniform acceleration? (ii) nonuniform acceleration?

10. A bus decreases its speed from 80 km/h to 60 km/h in 5 seconds. Find the acceleration of the bus.

11. A train starting from a railway station and moving with uniform acceleration attains a speed of 40 km/h in 10 minutes. Find its acceleration.

12. What is the nature of the distance-time graphs for uniform and non-uniform motion of an object?

13. What can you say about the motion of an object whose distance-time graph is a straight line parallel to the time axis?

14. What can you say about the motion of an object if its speed-time graph is a straight line parallel to the time axis?

15. What is the quantity which is measured by the area occupied below the velocity-time graph?

16. A bus starting from rest moves with a uniform acceleration of 0.1 m/s² for 2 minutes. Find (a) the speed acquired, (b) the distance travelled.

17. A train is travelling at a speed of 90 km/h. Brakes are applied so as to produce a uniform acceleration of -0.5 m/s². Find how far the train will go before it is brought to rest.

18. A trolley, while going down an inclined plane, has an acceleration of 2 cm/s². What will be its velocity 3 s after the start?

19. A racing car has a uniform acceleration of 4 m/s². What distance will it cover in 10 s after start?

20. A stone is thrown in a vertically upward direction with a velocity of 5 m/s. If the acceleration of the stone during its motion is 10 m/s² in the downward direction, what will be the height attained by the stone and how much time will it take to reach there?

21. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?

22. Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C?

23. Abdul, while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 30 km/h. What is the average speed for Abdul’s trip?

24. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s² for 8.0 s. How far does the boat travel during this time?

Exercise

1. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?

2. Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C?

3. Abdul, while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 30 km/h. What is the average speed for Abdul’s trip?

4. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s² for 8.0 s. How far does the boat travel during this time?

6. Fig 8.11 shows the distance-time graph of three objects A, B, and C. Study the graph and answer the following questions:

7. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m/s², with what velocity will it strike the ground? After what time will it strike the ground?

8. The speed-time graph for a car is shown as Fig. 8.12.

9. State which of the following situations are possible and give an example for each of these:

10. An artificial satellite is moving in a circular orbit of radius 42,250 km. Calculate its speed if it takes 24 hours to revolve around the earth.

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