Two cars are travelling towards each other at speed of 20 m s⁻¹ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s⁻². The distance between them when they come to rest is :

Solution

Physics sir · 3 steps

Find how far each car slides before stopping, then subtract both from the 300 m gap.

1. One car first. Each car starts at u = 20 m s⁻¹, ends at v = 0, and slows at a = 2 m s⁻². Time is not needed, so use the equation that links u, v, a and distance.

   s = u²/2a = (20)²/(2 × 2) = 100 m

2. Both cars together. The two cars are identical, so each covers 100 m before stopping. Together they close 100 + 100 = 200 m of the gap. This is less than 300 m, so they stop before they meet.
3. So. The gap left is 300 - 200 = 100 m, which is option (b).

The idea to keep. A body braking to rest covers u²/2a, no time needed. For two bodies closing a gap, add their stopping distances and compare the total with the starting separation.

Answer from the NTA final answer key. Solution by PrepWiser.