Calculate the work done by the brakes of a car of mass $1000\ kg$ when its speed is reduced from $20\ m/s$ to $10\ m/s$?

Here given, the mass of the car $m=1000\ kg$

Initial velocity of the car $v_1=20\ m/s$

Final velocity of the car $v_2=10\ m/s$

Therefore, work done by the brake to reduce the speed will be equal to the change in kinetic energy of the car.

Therefore, $W=K_1-K_2$

$=\frac{1}{2}mv_1^2-\frac{1}{2}mv_2^2$

$=\frac{1}{2}m(v_1^2-v_2^2)$

$=\frac{1}{2}\times1000(20^2-10^2)$

$=\frac{1}{2}\times1000(400-100)$

$=\frac{1}{2}\times1000\times300$

$=1.5\times10^5\ J$

Therefore, work done by the brakes will be $1.5\times10^5\ J$.