Question

You are driving to the grocery store at 18 m/s. You are 130 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 sand that your car brakes with constant acceleration.

What magnitude braking acceleration will bring you to a stop exactly at the intersection?

Answer 1

Your distance from the intersection = D = 130 m

Initial speed of the car = V₁ = 18 m/s

Reaction time = T₁ = 0.5 sec

Distance traveled by the car in the reaction time = D₁

D₁ = V₁T₁

D₁ = (18)(0.5)

D₁ = 9 m

Distance traveled by the car during the braking = D₂

You stop exactly at the intersection therefore the total distance traveled by the car is equal to the initial distance between you and the intersection.

D = D₁ + D₂

130 = 9 + D₂

D₂ = 121 m

Final speed of the car = V₂ = 0 m/s

Acceleration of the car while braking = a

V₂² = V₁² + 2aD₂

(0)² = (18)² + 2a(121)

a = -1.34 m/s²

Negative as it is deceleration.

We are asked for the magnitude of acceleration therefore it will be positive.

Magnitude of braking acceleration such that you come to a stop exactly at the intersection = 1.34 m/s²