Question

If Kelly the kater's speed increases so he has three times the momentum, then his kinetic energy increases by

A) 3 times
B) 6 times
C) 9 times
D) 12 times

Answer 1

If Kelly the skater's speed triples, resulting in three times the momentum, the kinetic energy will increase by a factor of 9, not 3, because kinetic energy is proportional to the square of the velocity.

Step-by-step explanation:

If Kelly the skater's speed increases such that he has three times the momentum, his kinetic energy will not simply triple, but rather increase by a factor more than three due to the relationship between momentum and kinetic energy. The kinetic energy (KE) is given by the equation KE = 1/2 mv2, where m is mass and v is velocity. Momentum (p), on the other hand, is given by the equation p = mv. If the momentum is tripled and the mass remains constant, the velocity must have also tripled because momentum is directly proportional to velocity.

Substituting the tripled velocity into the kinetic energy equation, we get KE = 1/2 m(3v)2 = 1/2 m(9v2) = 9(1/2 mv2), which means the kinetic energy increases by a factor of 9. Therefore, the correct answer would be C) 9 times.