Question

A bus and a car have a same kinetic energy which one of this w/o is moving faster
Explain

Answer 1

Let the car have a mass m and move with a velocity V. Let the bus have a mass M and move with a velocity v. Then,

Momentum of the car = m V,

Momentum of the bus= M v

Since the two momenta are equal we have,

mV = M v = p ( p is magnitude of momentum)

Kinetic energy of the car = p²/2m,………1

Kinetic energy of the bus= p²/2M, … ….2

Comparing equations 1 and 2,

Kinetic of the car › Kinetic energy of the bus ( as the kinetic energy of the vehicle is inversely proportional to the mass of the vehicle. A lighter vehicle has larger kinetic energy. Because to have the same momentum a lighter vehicle needs to travel much faster. And since Kinetic energy is proportional to square of velocity its kinetic energy is more than of the heavier vehicle).