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

A boy standing at the top of a tower of 20 m height drops a stone. Assuming g=$10 {\mathrm{ms}}^{-2}$, the velocity with which it hits the ground will be:
1. 20 m/s                                         
2. 40 m/s
3. 5 m/s                                           
4. 10 m/s

The motion of a particle along a straight line is described by the equation
         \(x=8+12 t-t^3\)

where \(x\) is in metre and t is in second. The retardation of the particle when its velocity becomes zero is:

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 particle is projected upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂ respectively. The velocity of projection will be:

1. gt₁

2. gt₂

3. $g$ $(t_1+t_2)$

4. $\frac{g(t_1+t_2)}{2}$

Four marbles are dropped from the top of a tower one after the other at a one-second interval. The first one reaches the ground after 4 seconds. When the first one reaches the ground the distances between the first and second, the second and third, and the third and fourth will be, respectively:

A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4h. The two stones cross each other after time:

1. $\sqrt{\frac{h}{8g}}$

2. $\sqrt{8g}$ $h$

3. $\sqrt{2g}$ $h$

4. $\sqrt{\frac{h}{2g}}$

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?

The acceleration of a particle starting from rest varies with time according to the relation A = – aω²sinωt. The displacement of this particle at a time t will be:

1. $-\frac{1}{2}\left({\mathrm{a\omega }}^2\mathrm{sin\omega t}\right){\mathrm{t}}^2$

2. $\mathrm{a\omega sin\omega t}$

3. $\mathrm{a\omega cos\omega t}$

4. $\mathrm{asin\omega t}$

Given below are two statements: