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.

what is her speed as she reaches light at the instant trund green?

Answer 1

The final speed at the gree light is 5.714 m/s

Step-by-step explanation:

Given that,

Initial speed of the motorist (U) = 20m/s

Displacement of the traffic light (S) = 200m

time taken to slam the brake (t₁) = 1s

Now, the displacement of the motorist, till she slams the brake

S₁ = U × t₁

= 20 × 1

= 20m

The remaining distance would be

S₂ = S - S₁

S₂ = 200 - 20

S₂ = 180m

Now, the deceleration of the motorist

S₂ = Ut + 1/2at²

180 = (20 × 14) + 0.5a(14)²

a = - 1.02m/s²

The final speed would be

v = u + at

v = 20 + (- 1.02)(14)

v = 5.714 m/s

The final speed at the gree light is 5.714 m/s