## Braking Force

A car that weighs 13700.0 N is initially moving at a speed of 57.0 km/hr when the brakes are applied and the car is brought to a stop in 4.1 s. Find the magnitude of the force that stops the car, assuming it is constant.

**5400 N**## Approach

When the brakes are applied, there is a force that slows the car down. This force is equal to mass times acceleration. Thus both the mass and the acceleration need to be determined.

## Solution

Given:

Weight W = 13700.0 N and since W = mg, mass m = W/g = 13700.0 N/(9.8 m/s2 = 1398.0 kg.

Initial speed v0 = 57.0 km/hr = 57.0/3.6 m/s = 15.83 m/s.

Final speed vf = 0 since the car comes to a stop.

Time to stop t = 4.1 s

The acceleration can be derived using vf = v0 + at, or...

a = (Vf-Vo)/t = (-15.83 m/s)/4.15s = - 3.862 m/s^2

The magnitude of the force is F = |ma| = (1398.0 kg)(3.862 m/s2) = 5400 N. (Magnitude means the absolute value.)

Weight W = 13700.0 N and since W = mg, mass m = W/g = 13700.0 N/(9.8 m/s2 = 1398.0 kg.

Initial speed v0 = 57.0 km/hr = 57.0/3.6 m/s = 15.83 m/s.

Final speed vf = 0 since the car comes to a stop.

Time to stop t = 4.1 s

The acceleration can be derived using vf = v0 + at, or...

a = (Vf-Vo)/t = (-15.83 m/s)/4.15s = - 3.862 m/s^2

The magnitude of the force is F = |ma| = (1398.0 kg)(3.862 m/s2) = 5400 N. (Magnitude means the absolute value.)