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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 $1.5\times10^5\ J$.
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