A bus moving along a straight highway with speed of 72 km / h is brought to halt within 4 s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ m.

Solution

Physics sir · 4 steps

Uniform retardation to rest means the average speed is just half the starting speed.

1. Convert to SI. 72 km/h = 72 × 5/18 = 20 m/s. The final speed is 0 and the time is 4 s.
2. Use average velocity. With uniform retardation, velocity falls linearly, so the average velocity is the mean of the initial and final values. You do not even need the acceleration.

   s = (u + v)/2 t = (20 + 0)/2 × 4 = 40 m

3. Cross-check. The retardation is a = 20/4 = 5 m s⁻², and s = ut - 1/2at² = 80 - 40 = 40 m. Same answer.
4. So. The bus travels 40 m before it stops.

The common slip: 80. Multiplying the full speed by the time, 20 × 4, gives 80, not 40. The bus slows down the whole way, so its average speed is only 10 m/s.

The idea to keep. Whenever acceleration is uniform and you know u, v and t, use s = (u+v)/2t. Always convert km/h to m/s first by multiplying by 5/18.

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