# 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

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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.

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).