Why is the equation for Kinetic Energy 1/2mv^2 when the equation for Momentum is mv?
In: Physics
Kinetic energy comes from applying a certain force over a certain distance. Momentum comes from applying a certain force over a certain time.
Now, lets say you’re at rest and a force accelerates you for 10 seconds. You will have covered some distance. Now if the same force accelerates you again for 10 seconds, you will have covered a greater distance the second time, because you were going faster the entire time. So your change in momentum from 0-10 and 10-20 is the same, since it’s the same force over the same time. But your change in kinetic energy is bigger for the second push since over those 10 seconds you were going faster and covered more distance. This gets translated into a v^2.
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