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 stay

Question

4 months ago

14

s 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.

1 answer:

Sav [3.1K] · Answer 1 · 2026-02-19T21:12:39+03:00

Answer:

$v = 5.72\ m/s$

Explanation:

Provided data:

The motorist's initial speed is 20 m/s.

The distance to the traffic light is 200 m.

The duration of the red light is 15 s.

It takes 1 s for the driver to apply the brakes.

Distance covered during this response time

d = s x t

d = 20 x 1 = 20 m

The time to arrive at the red light after factoring in the reaction time is 15 - 1 = 14 s.

The remaining distance to cover within this time is 200 - 20 = 180 m.

To determine the motorist's speed upon reaching the red light, employ the equation of motion

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

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

$98 a = -100$

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

Utilizing the equations of motion to ascertain the velocity:

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

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

$v = 5.72\ m/s$

The speed of the motorist as she reaches the red light is 5.72 m/s.

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