A driver takes 0.20 s to apply the brakes after seeing a need for it. This is termed 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/s ^2 , determine the distance travelled by the car after he sees the need to put the brakes on, in m.

Step-by-step solution

Initial speed of the car, u = 54 km/h = 54 5 18 m/s = 15 m/s Reaction time of the driver, t = 0.20 s Distance travelled during the reaction time, s₁ = u t = 15 0.20 = 3.0 m Deceleration of the car, a = -6.0 m/s ^2 Final velocity, v = 0 Using the equation of motion, v^2 - u^2 = 2as₂ 0 - (15)^2 = 2 (-6.0) s₂ s₂ = 225 12 = 18.75 m Total distance travelled by the car, s = s₁ + s₂ = 3.0 + 18.75 = 21.75 m