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## Monday, May 2, 2011

### Numerical Motion and Force and law of motion

1. A car moves 100 m due east and then 25 m due west, (a) What is the distance covered by the car? (b) What is its displacement?
2. A person walks along the sides of a square field. Each side is 100 m long. What is the maximum magnitude of displacement of the person in any time interval?
3. In the hare-tortoise race, the hare ran for 2 min at a speed of 7.5 km/h, slept for 56 min and again ran for 2 min at a speed of 7.5 km/h. Find the average speed of the hare in the race.
4. A bus takes 8 hours to cover a distance of 320 km. What is the average speed of the bus?
5. The maximum speed of a train is 80 km/h. It takes 10 hours to cover a distance of 400 km. Find the ratio of its maximum speed to its average speed.

6. An object moves through 10 m in 2 minutes and next 10 m in 3 minutes. Calculate its average speed.

7. A car moves through 20 km at a speed of 40 km/h, and the next 20 km at a speed of 60 km/h. Calculate its average speed.

8. A boy leaves his house at 9.30 a.m. for his school. The school is 2 km away and classes start at 10.00 a.m. If he walks at a speed of 3 km/h for the first kilometre, at what speed should he walk the second kilometre to reach just in time?
10. A bicycle increases its velocity from 10 km/h to 15 km/h in 6 seconds. Calculate its acceleration.
11. An object moves along a straight line with an acceleration of 2 m/s2. If its initial speed is 10 m/s, what will be its speed 5 s later?

12. An object dropped from a cliff falls with a constant acceleration of 10 m/s2. Find its speed 2 s after it was dropped.
13. A bullet hits a wall with a velocity of 20 m/s and penetrates it up to a distance of 5 cm. Find the deceleration of the bullet in the wall.
14. A train starts from a station and moves with a constant acceleration for 2 minutes. If it covers a distance of 400 m in this period, find the acceleration.
15. A ship moving with a constant acceleration of 36 km/h2 in a fixed direction speeds up from 12 km/h to 18 km/h. Find the distance traversed by the ship in this period.

16. A particle starts from a point with a velocity of +6.0 m/s and moves with an acceleration of -2.0 m/s2. Show that after 6 s the particle will be at the starting point.
17. A bicycle moves with a constant velocity of 5 km/h for 10 minutes and then decelerates at the rate 1 km/h2, till it stops. Find the total distance covered by the bicycle.
18. An object is moving along a straight line with a uniform speed of 10 m/s. Plot a graph showing distance versus time from t = 0 to t = 10 s.
19. A particle moves along a straight line with a uniform velocity of 5.0 m/s. Plot a distance-time graph for the period t = 0 to t = 5 s.
20. The driver of a car travelling at 36 km/h applies the brakes to decelerate uniformly. The car stops in 10 s. Plot the speed-time graph for this period. Find the distance travelled by the car during this period by calculating the area under the graph.
21. A particle moves along a straight line with a constant acceleration a = +0.5 m/s 2 At t = 0 it is at x = 0, and its velocity is v = 0. Plot the velocity-time and position-time graphs for the period t = 0 to t = 5 s.
23. The velocity-time graph of a particle moving along a straight line is given in Figure 2.E7. (a) Is the particle moving in the positive direction at t = 0? (b) Does the particle ever come to rest? If so, when? (c) Does the particle turn around? If so, when?