Question

A typical car under hard braking loses speed at a rate of about 6 m/s². The typical reaction time to engage the brakes is 0.50 s. A local school board sets the speed limit in a school zone such that all cars should be able to stop in 5.0 m. What maximum speed does this imply for a car in the school zone?

Answer 1

Let the maximum velocity be u

Using 3rd equation of motion

V^2 = u^2 - 2 a d. .. (I)

Stopping distance, d = 5 - ut = 5 - 0.5 u

Final velocity, v = 0 m/s

Putting in .. (I)

0 = u^2 - 2 * 6* ( 5 - 0.5 u)

u^2 + 6u - 60 = 0

u = 5.31 m/s

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