Question

A driver takes 0.20 s to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54 km/h and the brakes cause a deceleration of 6.0 m/s², find the distance travelled by the car after he sees the need to put the brakes on.

Answer 1

In the reaction time, the car moves with a constant speed of 54 km/h, i.e., 15 m/s.
Distance travelled in this time, s₁ = 15 × 0.2 = 3 m
When the brakes are applied:
Initial velocity of the car, u = 15 m/s
Final velocity of the car, v = 0
Acceleration, a = −6 m/s²
Distance, $s_2=\frac{v^2-u^2}{2a}$ = 18.75 m
Total distance, s = s₁ + s₂
⇒ s = 3 + 18.75 = 21.75 m
⇒ s$\approx$22 m