# Kinetic energy in frames of reference

1. Mar 11, 2005

### daveed

i was just reading, and i saw this question, and i dont know how to explain it....

how can you describe why when two things go at a velocity v, and one of them accelerates to 2v, the KE gain w/ respect to the earth and the other object are different, but the work done is constant?

i just dont know how to explain this... it should not be so difficult, no?

2. Mar 11, 2005

### SpaceTiger

Staff Emeritus
The work, Fx (assuming constant acceleration), isn't constant. The force is the same in both frames, but the distance isn't.

$$x=\int v~dt$$

Moving frame:

$$v=\int a~dt=at$$
$$x=\frac{1}{2}at^2$$

Stationary frame:

$$v=v_0+\int a~dt=v_0+at$$
$$x=v_0t+\frac{1}{2}at^2$$

In your example, this leads to work that's three times larger in the stationary frame, just like the change of kinetic energy.