Question

A 2000 kg car moving with initial speed 30 m/s is brought to rest in 25 seconds. What is the average power produced by the brakes in bringing the car to rest?

Answer 1

Take into account that the average power is given by:

`P=(F\cdot d)/(t)`

where F is the force, d is the distance and the t the time.

Then, it is necessary to calculate F. Use the following formula:

`F=m\cdot a`

m: mass of the car = 2000 kg

a: acceleration = ?

Calculate acceleration as follow:

`a=(v-v_o)/(t)=((0m)/(s)-(30m)/(s))/(25s)=1.2(m)/(s^2)`

where you have considered that the final velocity is 0m/s because the car stops.

Then, the force is:

`F=(2000kg)(1.2(m)/(s^2))=2400N`

Now, consider that it is necessary to calculate distance d in order to able to calculate P.

Calculate distance d as follow:

`d=(v^2_o)/(2a)=((30(m)/(s))^2)/(2(1.2(m)/(s^2)))=375m`

Then, by replacing d, F and t = 25 s, you obtain for the power:

`P=(2400N\cdot375m)/(25s)=36000W=36kW`

Hence, the average power produced by the brakes was 36kW