# The car began to brake at a speed of 54 km / h. After what period of time will it stop completely

The car began to brake at a speed of 54 km / h. After what period of time will it stop completely if the braking distance is 75 meters?

V0 = 54 km / h = 15 m / s.

V = 0 m / s.

S = 75 m.

t -?

The braking time of the car t is expressed from the formula for acceleration: a = (V0 – V) / t, where V0, V are the initial and final speed during braking.

t = (V0 – V) / a.

The acceleration of the car a during braking is expressed by the formula: a = (V0 ^ 2 – V ^ 2) / 2 * S.

t = (V0 – V) 2 * S / (V0 ^ 2 – V ^ 2) = (V0 – V) * 2 * S / (V0 – V) * (V0 + V) = 2 * S / (V0 + V).

t = 2 * 75 m / (15 m / s – 0 m / s) = 10 s.

Answer: the time of braking the car to a complete stop is t = 10 s.

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