What happens to the cart's kinetic energy when the mass/velocity of the cart triples?

Question

A cart with a mass of M is traveling at a velocity of V.

 

a) What happens to the cart's kinetic energy when the mass of the cart triples?

b) What happens to the cart's kinetic energy when the velocity of the cart triples?

Answer 1

The equation KE = ½ mv² shows that the relationship between Kinetic Energy and mass is directly proportional.

a)So if the mass triples then the KE triples too.

The relationship between Kinetic Energy and velocity is also directly proportional but with the square of the velocity.

b) So if the velocity triples, then it is 3² , three squared or 9. Hence, KE is 9 times greater.