By what factor does the kinetic energy of a car change when its speed is tripled?Multiple Choice: a) factor of 3 b) factor of 6 c) factor of 9 d) factor of 12

2 Answers | Add Yours

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

The correct answer here is C -- it increases by a factor of 9.  Here's why:

The formula for kinetic energy is

k = .5 mv^2 or k = .5*m*v*v

Where k is kinetic energy, m is the mass and v is the velocity.

If me assume that the mass of the car does not change as its speed changes, the only thing that changes is the velocity.

When the velocity triples, the kinetic energy goes up by a factor of 9 because the velocity gets squared while mass remains constant.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

If the car speed is v m/s and its kinetic energy is given by: k1= (1/2)mv^2, where v is the nass of car.

If the speed is trippled is the speed is 3v. Its kinetic energy at his speed is given by K3 = (1/2)m(3v)^2 (9/2)mv^2

Therefore, the factor by which the kinetic energy chaged is:

K2 k1 = (9/2)mv^2 /[(1/2)mv^2] =  9. The correct choice is at (c).

We’ve answered 317,615 questions. We can answer yours, too.

Ask a question