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?

Two balls are projected upward simultaneously with speeds of 40 m/s and 60 m/s. Relative position (x) of the second ball with respect to the first ball at time t = 5 sec will be: [Neglect air resistance]

1. 20 m

2. 80 m

3. 100 m

4. 120 m

Two trains, each 50 m long, are travelling in the opposite direction with velocities 10 m/s and 15 m/s. The time of crossing is:

1. 10 sec

2. 4 sec

3. $2\sqrt{3}$ $\sec$

4. $4\sqrt{3}$ $\sec$

The distance between two particles is decreasing at the rate of 6 m/sec when they are moving in the opposite directions. If these particles travel with the same initial speeds and in the same direction, then the separation increases at the rate of 4 m/sec. It can be concluded that particles' speeds could be

1. 5 m/sec, 1 m/sec

2. 4 m/sec, 1 m/sec

3. 4 m/sec, 2 m/sec

4. 5 m/sec, 2 m/sec

Two cars are moving in the same direction with the same speed 30 km/hr. They are separated by a distance of 5 km. The speed of a car moving in the opposite direction, if it meets these two cars at an interval of 4 minutes, will be

1. 40 km/hr

2. 45 km/hr

3. 30 km/hr

4. 15 km/hr

A bus is moving with a speed of $10$ ${\mathrm{ms}}^{}$ $-1$ on a straight road. A scooterist wishes to overtake the bus in $100$ $\mathrm{s}$. If the bus is at a distance of $\mathrm{1 }\mathrm{km}$ from the scooterist, with what minimum speed should the scooterist chase the bus?

1. 20 ms^-1

2. 40 ms^-1

3. 25 ms^-1                                         

4. 10 ms^-1

Two trains each of length 100 m are moving parallel towards each other at speeds 72 km/h and 36 km/h respectively. In how much time will they cross each other?

1. 4.5 s

2. 6.67 s

3. 3.5 s

4. 7.25 s

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

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\). On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk upon the moving escalator will be:
1. \(\frac{t_1t_2}{t_2-t_1}\)
2. \(\frac{t_1t_2}{t_2+t_1}\)
3. \(t_1-t_2\)
4. \(\frac{t_1+t_2}{2}\)

A car A is traveling on a straight level road at a uniform speed of 60 km/h. It is followed by another car B which is moving at a speed of 70 km/h. When the distance between them is 2.5 km, car B is given a deceleration of 20 km/h². After how much time will car B catch up with car A?

1. 1 hr

2. 1/2 hr

3. 1/4 hr

4. 1/8 hr