An elevator car, whose floor to ceiling distance is equal to \(2.7~\text{m}\), starts ascending with constant acceleration of \(1.2~\text{ms}^{-2}\). \(2\) sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is: 
1. \(\sqrt{0.54}~\text{s}\)
2. \(\sqrt{6}~\text{s}\)
3. \(0.7~\text{s}\)
4. \(1~\text{s}\)

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 ball is thrown vertically upwards with a velocity \(u\) with respect to ground from a balloon descending with velocity \(v\) with respect to ground. The ball will pass the balloon after time:
1. \(\frac{u-v}{2g}\)
2. \(\frac{u+v}{2g}\)
3. \(\frac{2(u-v)}{g}\)
4. \(\frac{2(u+v)}{g}\)

A boy falls from a building of height \(320\) m. After \(5\) seconds, superman jumps downward with initial speed \(u\) such that the boy can be saved. The minimum value of \(u\) is: (assume \(g= 10~\text{m/s}^2\)${\mathrm{}}^{}$)

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

A bus is moving with a speed of \(10~\text{ms}^{-1}\) on a straight road. A scooterist wishes to overtake the bus in \(100~\text{s}\)$\mathrm{}$. If the bus is at a distance of \(1~\text{km}\) from the scooterist, with what minimum speed should the scooterist chase the bus?
1. \(20~\text{ms}^{-1}\)
2. \(40~\text{ms}^{-1}\)
3. \(25~\text{ms}^{-1}\)
4. \(10~\text{ms}^{-1}\)

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. \(\frac{1}{2}\) hr
3. \(\frac{1}{4}\) hr
4. \(\frac{1}{8}\) hr

Suppose you are riding a bike with a speed of \(20~\text{m/s}\) 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 \(30~\text{m/s}\) due east, then the relative velocity between two reference frames \(A\) and \(B\) is:

A jet airplane travelling at the speed of \(500~\text{km/h}\) ejects its products of combustion at the speed of \(1500~\text{km/h}\) relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?
1. \(1000~\text{km/h}\)
2. \(500~\text{km/h}\)
3. \(1500~\text{km/h}\)
4. \(2000~\text{km/h}\)$\mathrm{}$

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. \(4.5~\text{s}\) 
2. \(6.67~\text{s}\)
3. \(3.5~\text{s}\)
4. \(7.25~\text{s}\)