Question

Calculate the work done by the brakes of a gas of mass 1000 kg when its speed in reduced from 20 m/s or 10 m/s?

Answer 1

Mass of a car = 1000 kg

We have to calculate the work done by the brakes when the speed of the car is reduced from 20 m/s to 10 m/s.Let,

v₁ = 20 m/s v₂ = 10 m/s

The kinetic energy of the car when its speed is 20 m/s is given as:

K₁ = 1/2 m v₁²

K₁ = 1/2 (1000) (20)²

K₁ = 2 x 10⁵ J

The kinetic energy of the car when its speed is reduced to 10 m/s is given as:

K₂ = 1/2 m v₂²

K₂ = 1/2 (1000) (10)²

K₂ = 5 x 10⁴ J

So, the work done by the brake will be the difference of their kinetic energies.

Therefore,

K₂ - K₁ = 5 x 10⁴ - 2 x 10⁵

K₂ - K₁ = - 150,000 J

So, work done by the brakes to reduce the speed of the car from 20 m/s to 10 m/s is (- 150,000) J.

It's negative because the brakes oppose the motion of the car