Question

A driver has a reaction time of 0.50 s , and the maximum deceleration of her car is 6.0 m/s^2 . She is driving at 20 m/s when suddenly she sees an obstacle in the road 50 m in front of her. What is the distance she passes after noticing the obstacle before fully stopping? Express your answer with the appropriate units.

Answer 1

Answer:

The car stops after 32.58 m.

Explanation:

t = Time taken for the car to stop

u = Initial velocity = 20 m/s

v = Final velocity = 0

s = Displacement

a = Acceleration = -6 m/s²

Time taken by the car to stop

$v=u+at\\\Rightarrow t=\frac{v-u}{a}\\\Rightarrow t=\frac{0-20}{-6}\\\Rightarrow t=3.33\ s$

Total Time taken by the car to stop is 0.5+3.33 = 3.83 s

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=20\times 3.83+\frac{1}{2}\times -6\times 3.83^2\\\Rightarrow s=32.58\ m$

The car stops after 32.58 m.

Distance between car and obstacle is 50-32.58 = 17.42 m