A driver has a reaction time of 0.50s, and the maximum deceleration of her car is 6.0m/s2. She is driving at 20m/s when suddenly she sees an obstacle in the road 50m in front of her.

Can she stop the car in time to avoid the collision?

given,

reaction time. t_r = 0.50 s

deceleration of the car = 6 m/s²

initial speed, v = 20 m/s

distance at which the car stop = ?

distance travel by the car in reaction time

d = v x t_r

d = 20 x 0.5 = 10 m

using equation of motion

distance travel to stop the car

v² = u² + 2 a s

0² = 20² - 2 x 6 x s

12 s = 400

s = 33.33 m

Total distance travel by the car

D = 10 + 33.33

D = 43.33 m

Hence, the car stops before to avoid collision.