With what acceleration did the car move during emergency braking if its speed before braking was 72 km / h

With what acceleration did the car move during emergency braking if its speed before braking was 72 km / h, and the braking distance was 20 m? How long did it take before it came to a complete stop?

Given:

v = 72 km / h = 20 m / s – vehicle speed before braking;

S = 20 meters – braking distance of the vehicle.

It is required to determine the vehicle acceleration a (m / s ^ 2) and the time to a complete stop t (seconds).

S = V * t – a * t ^ 2/2 = V * V / a – a * V ^ 2 / (2 * a ^ 2) = V ^ 2 / a – V ^ 2 / (2 * a) = V ^ 2 / (2 * a), hence:

a = V ^ 2 / (2 * S) = 20 ^ 2 / (2 * 20) = 20/2 = 10 m / s ^ 2.

The time to a complete stop is equal to:

t = V / a = 20/10 = 2 seconds.

Answer: the car was moving with an acceleration of 10 m / s ^ 2, the time until the car came to a complete stop is 2 seconds.