Answer to Question #119736 in Classical Mechanics for Brandon

Question

Determine the amount of kinetic energy absorbed by the brakes when a car is travelling at 60km/hr and brakes to 40km/hr?

Answer 1

The initial speed of the car is $u=60Km/hr=\frac{50}{3}m/s$ ,final speed is $v=40Km/hr=\frac{100}{9}m/s$ .

Since, mass of the car is not provided, we assume mass be $m=1Kg$

Let work(energy) done(absorbed) by the brake is $W_b$ ,

Thus by law of conservation of energy we get,

$$\frac{1}{2}mu^2=\frac{1}{2}mv^2 + W_b\\ \implies W_b=\frac{1}{2}mu^2-\frac{1}{2}mv^2$$

Thus on plugin the value we get,

$$W_b=\frac{1}{2}\bigg(\frac{50}{3}\bigg)^2-\frac{1}{2}\bigg(\frac{100}{9}\bigg)^2\\ \implies W_b=77.16J$$