Question

A motorist is driving at 20m/s when she sees that a traffic light 200m ahead has just turned red. She knows that this light stays red for 15s, and she wants to reach the light just as it turns green again. It takes her 1.0s to step on the brakes and begin slowing.

Answer 1

Answer:

$v = 5.72\ m/s$

Explanation:

given,

initial speed of the motorist = 20 m/s

distance of the traffic light = 200 m

time of which red light stays = 15 s

time taken to step on brake = 1 s

distance travel in this time

d = s x t

d = 20 x 1 = 20 m

time taken to reach the red light after reaction time= 15 -1 = 14 s

distance to travel in 14 s = 200 -20 = 180 m

to calculate the speed of the motorist when it reaches the red light.

using equation of motion

$s = u t + \dfrac{1}{2}at^2$

$180 =20\times 14 + \dfrac{1}{2}\times a\times 14^2$

$98 a = -100$

$a = -1.02\ m/s^2$

using equation of motion to calculate the velocity

$v^2 = u^2 + 2 a s$

$v^2 = 20^2 - 2\times 1.02\times 180$

$v = 5.72\ m/s$

Speed of motorist when it reaches red light is equal to 5.72 m/s.