Question

The mass of car 2 is twice the mass of car 1. If both cars have the same velocity, how does the kinetic energy of car 2 compare to car 1?

Car 2 has four times the kinetic energy.
Car 2 has twice the kinetic energy.
Both cars have the same kinetic energy.
Both cars increase in kinetic energy if they slow down.

Answer 1

The answer is Car 2 has twice the kinetic energy.

Answer 2

m₁ = mass of car 1 = m

m₂ = mass of car 2 = 2 m

v₁ = speed of car 1 = v₂ = speed of car 2 = v

Kinetic energy of car 1 is given as

KE₁ = (0.5) m₁ v₁²

KE₁ = (0.5) m v² eq-1

Kinetic energy of car 2 is given as

KE₂ = (0.5) m₂ v₂²

KE₂ = (0.5) (2m) (v)²

KE₂ = 2 (0.5) m v²

Using eq-1

KE₂ = 2 KE₁

hence the correct choice is

Car 2 has twice the kinetic energy.