Two trains \(A\) and \(B\) of length \(400~\text m\) each are moving on two parallel tracks with a uniform speed of \(72~\text{km/h}\) in the same direction with \(A\) ahead of \(B.\) The driver of \(B\) decides to overtake \(A\) and accelerates by \(1~\text{m/s}^2.\) If after \(50~\text s,\) the guard of \(B\) just brushes past the driver of \(A,\) what was the original distance between them?
1. \(2000~\text m\)
2. \(2250~\text m\)
3. \(1200~\text m\)
4. \(1250~\text m\)

On a two-lane road, car \(A\) is travelling at a speed of \(36~\text{km/h}.\) Two cars \(B\) and \(C\) approach car \(A\) in opposite directions with a speed of \(54~\text{km/h}\) each. At a certain instant, when the distance \(AB\) is equal to \(AC,\) both being \(1~\text{km},B\) decides to overtake \(A\) before \(C\) does. What minimum acceleration of car \(B\) is required to avoid an accident?
1. \(1~\text{m/s}^{2}\)
2. \(5~\text{m/s}^{2}\)
3. \(2~\text{m/s}^{2}\)
4. \(3~\text{m/s}^{2}\)

A player throws a ball upwards with an initial speed of \(29.4 \text{ ms}^{- 1}.\) What is the direction of acceleration during the upward motion of the ball?
1. Vertically downwards
2. Vertically upwards
3. First upwards then downwards
4. None of the above

A particle in one-dimensional motion:

A man walks on a straight road from his home to a market \(2.5\) km away with a speed of \(5\) km/h. Finding the market closed, he instantly turns and walks back home with a speed of \(7.5\) km/h. What is the magnitude of the average velocity of the man over the interval of time \(0\) to \(30\) min?

The instantaneous speed is always:

A police van moving on a highway with a speed of $30<mspace\; width="1em"></mspace>km<mspace\; width="1em"></mspace>h^{-1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of $192<mspace\; width="1em"></mspace>km<mspace\; width="1em"></mspace>h^{-1}$. If the muzzle speed of the bullet is $150<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace>s^{-1},$ with what speed does the bullet hit the thief’s car? 

$\left(1\right)<mspace\; width="1em"></mspace>103<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace>s^{-1}$
$\left(2\right)<mspace\; width="1em"></mspace>105<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace>s^{-1}$
$\left(3\right)<mspace\; width="1em"></mspace>101<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace>s^{-1}$
$\left(4\right)<mspace\; width="1em"></mspace>102<mspace\; width="1em"></mspace>m<mspace\; width="1em"></mspace>s^{-1}$

The figure gives the \((x\text-t)\) plot of a particle in a one-dimensional motion. Three different equal intervals of time are shown. The signs of average velocity for each of the intervals \(1,\) \(2\) and \(3,\) respectively are:
                       

The figure gives a speed-time graph of a particle in motion along the same direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude?

A boy standing on a stationary lift (open from above) throws a ball upwards with the maximum initial speed he can, equal to \(49~\text{ms}^{-1}.\) How much time does the ball take to return to his hands?