It is my understanding that to calculate the change of kinetic energy of an object that speeds up from vi to vf you use this formula: Change of kinetic energy = 1/2 * m * (vf2 - vi2) When the initial velocity is 0 m/s I have no problems, but let's say an object that weighs 2 kg speeds up from 20 m/s to 40 m/s. When I use the formula I mentioned, I get: ΔEk = 1/2 * 2 * (1600 - 400) = 1200 J Now let's say the initial velocity is 0 m/s, final 20 m/s. I then get: ΔEk = 1/2 * 2 * (400 - 0) = 400 J Does this make sense? The same changes in velocity and different changes in kinetic energy? Should I not use a formula like this instead: ΔEk = 1/2 * m * (Δv)2 = 1/2 * m * (vf - vi)2 ? Then I end up with 400 J in both cases. Also, what if the initial velocity is, lets's say 5 m/s and final -5 m/s? Does the kinetic energy change?