# Kinetic energy in frames of reference

## Main Question or Discussion Point

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?

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SpaceTiger
Staff Emeritus
Gold Member
daveed said:
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?
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.