Physics Question

Question

A driver in a car traveled at a speed of 21.8 m/s sees a cat 100m away on the road. How long will it take for the car to accelerate uniformly to stop in exactly 99m?

Answer 1

As we know: V² - V₀² = 2aX , V is the final speed which will be zero at X=99 m.

- V₀² = 2a. (99m) → a = - (V₀²) / (2×99) , a = - (21.8)² / (198) = - 2.4 m/s²

V = a.t + V₀ → 0 = (-2.4).t + 21.8 → t = (-21.8) / (-2.4) = 9.083 sec

Second Method:

X = [(V+V₀) / 2 ]. t (this formula is correct only for constant acceleration motion)

V=0 is final speed at X = 99 m which the car must stop.

99 = (21.8 / 2 ) . t → t = 9.083 sec