1. The problem statement, all variables and given/known data I'm actually making up my own problem here to try to resolve some confusion I'm running into on understanding kinetic energy and reference frames.... Let's launch a potato of mass m (just call it 1) horizontally with a potato gun on a fast vehicle moving 50 m/s, while I'm watching and measuring from a stationary position. I want to see a potato flying by at 100m/s. Assume that whatever potential energy is "charged" in the gun is fully transferred into kinetic energy of the potato. How much energy do I need to precharge the gun with before putting it on the vehicle and having it fired? 2. Relevant equations KE=1/2 mv^2 3. The attempt at a solution I assume that both the moving vehicle and my stationary position are valid inertial reference frames. From a reference frame of my position on the ground, then it would appear that the KE needed to add to the potato to go from 50m/s (vehicle speed) to 100m/s (post-launch speed) is KE = 1/2 * 1 * 100^2 - 1/2 * 1 * 50*2 = 3750J From the reference frame of the vehicle, it would appear that the potato only would need to go from the "apparent standstill" of 0m/s up to 50m/s, which would require 1/2 * 1 * 50^2 = 1250J Of course, these reference frames are moving 50m/s relative to each other, which changes the KE of the potato measured relative to observers in each frame. But here's where I get confused in my example... From my stationary point of view, I need the gun to accelerate a potato from 50 to 100 m/s, and so would need to add 3750J. But from a vehicle occupant's point of view, it would only need to accelerate from 0 to 50m/s, and so need 1250J added. Both inertial reference frames are equally valid. The change in velocity is the same in each case (0 to 50 or 50 to 100), while only the absolute velocity range being looked at is different. But the end result from the stationary view is simply a potato moving at 100m/s. So to see the result I want, when I hand off the potato gun into the vehicle, do I pre-charge the potato gun with 1250J or with 3750J? Or put another way, from the stationary reference frame, it seems the vehicle's motion contains the 1250J (doing the initial accelerating from 0 to 50 within the vehicle) and the gun needs to add the 3750J, while from the vehicle's reference frame, the moving vehicle seems to give the potato the 3750J based on the stationary viewer and the gun only needs to add the 1250J. In any case, the potato should end up with KE = 5000J and going 100m/s relative to the stationary observer.