Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2 (v_1>v_2)\). When the car \(A\) is at a distance \(d\) behind car \(B\), the driver of the car \(A\) applied the brake producing uniform retardation \(a\). There will be no collision when:
1. \(d< \dfrac{(v_1-v_2)^2}{2a}\)

2. \(d< \dfrac{v^2_1-v^2_2}{2a}\)

3. \(d> \dfrac{(v_1-v_2)^2}{2a}\)

4. \(d> \dfrac{v^2_1-v^2_2}{2a}\)

A man is \(45\ \text{m}\) behind the bus when the bus starts accelerating from rest with an acceleration of \(2.5\ \text{m/s}^2\). With what minimum velocity should the man start running to catch the bus?

1.  \(12\ \text{m/s}\)
2.  \(14\ \text{m/s}\)
3.  \(15\ \text{m/s}\)
4.  \(16\ \text{m/s}\)

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

A \(120\ \text{m}\) long train is moving in a direction with speed \(20\ \text{m/s}\). A train \(B\), moving with \(30\ \text{m/s}\) in the opposite direction and \(130\ \text{m}\) long, crosses the first train in a time:

1.  \(4\ \text{s}\)
2.  \(36\ \text{s}\)
3.  \(38\ \text{s}\)
4.  \(5\ \text{s}\)

A \(210\) meter long train is moving due north at a speed of \(25\ \text{m/s}\). A small bird is flying due South a little above the train with a speed of \(5\ \text{m/s}\). The time taken by the bird to cross the train is:

1. \(6\ \text{s}\)
2. \(7\ \text{s}\)
3. \(9\ \text{s}\)
4. \(10\ \text{s}\)