Numerical problems in the field of motion for Class 9 involve applying mathematical concepts to understand and solve real-world scenarios related to objects in motion. These problems help students develop skills in calculating speed, velocity, distance, time, and acceleration. By solving these numericals, students gain a deeper understanding of the principles of motion and how various factors influence the movement of objects. They also learn to analyze and interpret data, enhancing their problem-solving and critical thinking abilities in the context of motion.
Numericals of Motion Class 9
1. A car travels a distance of 300 meters in 20 seconds. Calculate its average speed.
Ans: Average speed = Total distance / Total time
Average speed = 300 meters / 20 seconds
Average speed = 15 meters per second
2. A train covers a distance of 450 kilometers in 5 hours. Find its average speed.
Ans: Average speed = Total distance / Total time
Average speed = 450 kilometers / 5 hours
Average speed = 90 kilometers per hour
3. An object moves with a uniform velocity of 10 meters per second for 15 seconds. Calculate the distance covered by the object.
Ans: Distance covered = Velocity x Time
Distance covered = 10 meters per second x 15 seconds
Distance covered = 150 meters
4. A ball is dropped from a height of 40 meters. Calculate the time it takes to reach the ground. (Assume no air resistance)
Ans: To calculate the time taken to reach the ground, we can use the equation of motion:
Distance = (Initial velocity x Time) + (0.5 x Acceleration x Time^2)
Here, the initial velocity is 0 m/s (since it’s dropped), the distance is 40 meters, and acceleration due to gravity is approximately 9.8 m/s^2.
40 meters = (0 x Time) + (0.5 x 9.8 x Time^2)
40 = 4.9 x Time^2
Time^2 = 40 / 4.9
Time ≈ √(40 / 4.9)
Time ≈ √8.163
Time ≈ 2.86 seconds (approx.)
5. A cyclist covers a distance of 12 kilometers in 30 minutes. Calculate the average speed of the cyclist in meters per second.
Ans: Average speed = Total distance / Total time
Convert 30 minutes to hours: 30 minutes = 30/60 = 0.5 hours
Average speed = 12 kilometers / 0.5 hours
Average speed = 24 kilometers per hour
6. A sprinter runs a distance of 200 meters in 25 seconds. Calculate the average speed of the sprinter.
Answer:
Average speed = Total distance / Total time
Average speed = 200 meters / 25 seconds
Average speed = 8 meters per second
7. A car accelerates uniformly from rest to a speed of 25 meters per second in 10 seconds. Find its acceleration.
Answer:
Acceleration = Change in velocity / Time
Change in velocity = Final velocity – Initial velocity
Change in velocity = 25 m/s – 0 m/s = 25 m/s
Acceleration = 25 m/s / 10 s
Acceleration = 2.5 m/s²
8. A train takes 4 hours to travel a distance of 400 kilometers. Calculate its average speed.
Answer:
Average speed = Total distance / Total time
Average speed = 400 kilometers / 4 hours
Average speed = 100 kilometers per hour
9. An object is thrown vertically upward with an initial velocity of 20 meters per second. Calculate the time it takes for the object to reach its maximum height. (Neglect air resistance)
Answer:
The time taken to reach the maximum height is equal to the time taken for the vertical velocity to become zero.
Initial velocity = 20 m/s
Acceleration due to gravity = -9.8 m/s² (negative sign indicates upward motion)
Using the equation: Final velocity = Initial velocity + (Acceleration x Time)
0 = 20 m/s – 9.8 m/s² x Time
Time = 20 m/s / 9.8 m/s²
Time ≈ 2.04 seconds (approx.)
10. A cyclist covers a distance of 15 kilometers in 45 minutes. Calculate the average speed in meters per second.
Answer:
Convert 45 minutes to hours: 45 minutes = 45/60 = 0.75 hours
Average speed = Total distance / Total time
Average speed = 15 kilometers / 0.75 hours
Average speed = 20 kilometers per hour
Convert kilometers per hour to meters per second:
1 kilometer per hour = (1000 meters) / (3600 seconds) = 1/3.6 meters per second
Average speed = 20 kilometers per hour x (1/3.6) meters per second
Average speed ≈ 5.56 meters per second (approx.)
11. A ball rolls down a slope and covers a distance of 120 meters in 10 seconds. Calculate its average speed.
Answer:
Average speed = Total distance / Total time
Average speed = 120 meters / 10 seconds
Average speed = 12 meters per second
12. A car decelerates uniformly from a speed of 30 meters per second to rest in 5 seconds. Find its deceleration.
Answer:
Deceleration = Change in velocity / Time
Change in velocity = Final velocity – Initial velocity
Change in velocity = 0 m/s – 30 m/s = -30 m/s (negative sign indicates deceleration)
Deceleration = -30 m/s / 5 s
Deceleration = -6 m/s²
13. A bullet fired from a gun travels a horizontal distance of 600 meters in 10 seconds. Calculate its velocity.
Answer:
Velocity = Distance / Time
Velocity = 600 meters / 10 seconds
Velocity = 60 meters per second
14. An object is thrown horizontally from a height of 20 meters with an initial velocity of 10 meters per second. Calculate the time it takes to reach the ground. (Neglect air resistance)
Answer:
The horizontal velocity does not affect the time of flight. The time taken to reach the ground is the same as the time taken for an object to fall vertically from the same height.
Using the equation: Distance = (Acceleration x Time^2) / 2
Distance = 20 meters
Acceleration due to gravity = 9.8 m/s² (downward direction)
20 meters = (9.8 m/s² x Time^2) / 2
Time^2 = (20 meters x 2) / 9.8 m/s²
Time ≈ √(40 / 9.8)
Time ≈ √4.082
Time ≈ 2.02 seconds (approx.)
15. A train accelerates uniformly from rest and reaches a speed of 40 meters per second in 20 seconds. Calculate its acceleration.
Answer:
Acceleration = Change in velocity / Time
Change in velocity = Final velocity – Initial velocity
Change in velocity = 40 m/s – 0 m/s = 40 m/s
Acceleration = 40 m/s / 20 s
Acceleration = 2 m/s²
These are the answers to the additional set of numerical problems.
16. A cyclist covers a distance of 80 kilometers in 4 hours. Calculate the average speed in meters per second.
Answer:
Convert 80 kilometers to meters: 80 kilometers = 80,000 meters
Average speed = Total distance / Total time
Average speed = 80,000 meters / 4 hours = 20,000 meters per hour
Convert meters per hour to meters per second:
1 meter per hour = (1 meter) / (3600 seconds) = 1/3600 meters per second
Average speed = 20,000 meters per hour x (1/3600) meters per second
Average speed ≈ 5.56 meters per second (approx.)
17. A car travels a distance of 150 meters with a constant velocity of 20 meters per second. Calculate the time taken to cover this distance.
Answer:
Time = Distance / Velocity
Time = 150 meters / 20 meters per second
Time = 7.5 seconds
18. An object is dropped from a height of 80 meters. Calculate the time it takes to reach the ground. (Assume no air resistance)
Answer:
The time taken to reach the ground can be calculated using the equation: Time = √(2h/g)
where h is the height and g is the acceleration due to gravity (approximately 9.8 m/s²).
Time = √(2 x 80 meters / 9.8 m/s²)
Time ≈ √(16.33)
Time ≈ 4.04 seconds (approx.)
19. A train decelerates uniformly from a speed of 30 meters per second to rest in 10 seconds. Find its deceleration.
Answer:
Deceleration = Change in velocity / Time
Change in velocity = Final velocity – Initial velocity
Change in velocity = 0 m/s – 30 m/s = -30 m/s (negative sign indicates deceleration)
Deceleration = -30 m/s / 10 s
Deceleration = -3 m/s²
20. A runner completes one lap around a circular track with a circumference of 400 meters in 2 minutes. Calculate the average speed in kilometers per hour.
Answer:
Convert 2 minutes to hours: 2 minutes = 2/60 = 1/30 hours
Distance covered in one lap = Circumference of the track = 400 meters
Average speed = Total distance / Total time
Average speed = 400 meters / (1/30) hours = 400 x 30 meters per hour
Convert meters per hour to kilometers per hour:
1 kilometer = 1000 meters
Average speed = (400 x 30) meters per hour / 1000 = 12 kilometers per hour
These are the answers to the additional set of numerical problems.