The amount of energy is, in fact, the same. Let's go with a 10kg mass from 0 to 20 meters/second (about 45mph) and let's accelerate it at 10m/s2 and 5m/s2. It's not f=ma we need to use, it's how much kinetic energy do we need to put into the mass to get it to 20m/s? That formula is E=1/2mv2 and...