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 \(36\) kmh^–1. Two cars \(B\) and \(C\) approach car \(A\) in opposite directions with a speed of \(54\) kmh^–1 each. At a certain instant, when the distance \(AB\) is equal to \(AC\), both being \(1\) km, \(B\) decides to overtake \(A\) before \(C\) does. What minimum acceleration of car \(B\) is required to avoid an accident?
1. \(1\) ms^–2
2. \(5\) ms^–2
3. \(2\) ms^–2
4. \(3\) ms^–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?