By what factor does an object's kinetic energy change if its speed is doubled?

Question

By what factor does an object's kinetic energy change if its speed is doubled? By what factor does its momentum change?

Answer 1

Look at it this way:

KE=1/2mv^2

That's your initial energy. Now double the speed:

KE'=1/2m(2v)^2
= 1/2mv^2(4)

That's the energy when speed is doubled. If you now compare the two quantities, you will note that KE' is 4 times KE. So double the speed and KE is quadrupled.


Momentum=mv

Now double the speed:

Momentum'=mv2

Again compare the two quantities. You will note that momentum' is 2 times the originial momentum. So double the speed and you double the momentum.

Answer 2

4 for the energy (function of the speed squared)
and momentum is doubled (function of the speed)

Answer 3

4 x's
ke = 1/2 m v^2
Doulbe the velocity 4x's the energy