A thief is running away on a straight road in a jeep moving with a speed of 9 ms^–1. A policeman chases him on a motor cycle moving at a speed of 10 ms^–1. If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the policeman to catch the thief?

An elevator whose floor to ceiling height is 12 meters, moves upward with an acceleration of $2.2$ $\mathrm{m}/{\mathrm{s}}^2$. After 1.5 seconds since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is

1. 1 s

2. 2 s

3. $\sqrt{2}$ s

4. $\sqrt{3}$ s

Suppose you are riding a bike with a speed of 20 m/s due east relative to a person A who is walking on the ground towards the east. If your friend B walking on the ground due west measures your speed as 30 m/s due east, find the relative velocity between two reference frames A and B:-

1. The velocity of A with respect to B is 5 m/s towards the east

2. The velocity of A with respect to B is 5 m/s towards the west

3. The velocity of A with respect to B is 10 m/s towards the east

4. The velocity of A with respect to B is 10 m/s towards the west

Two cars A and B are travelling in the same direction with velocities v₁ and v₂ $(v_1>v_2)$. When the car A is at a distance d behind car B, the driver of the car A applied the brake producing uniform retardation a. There will be no collision when-

1. $d<\frac{{(v_1-v_2)}^2}{2a}$

2. $d<\frac{v_1^2-v_2^2}{2a}$

3. $d>\frac{{(v_1-v_2)}^2}{2a}$

4. $d>\frac{v_1^2-v_2^2}{2a}$ 

A ball is bouncing elastically with a speed of 1 m/s between the walls of a railway compartment of size 10 m in a direction perpendicular to the walls. The train is moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground:
(a) the direction of motion of the ball changes every 10 sec.
(b) the speed of the ball changes every 10 sec.
(c) the average speed of the ball over any 20 sec intervals is fixed.
(d) the acceleration of the ball is the same as from the train.
Choose the correct option:
1. (a), (c), (d)
2. (a), (c)
3. (b), (c), (d)
4. (a), (b), (c)