Why is the kinetic energy of an object proportional to the square of the velocity? I’ve read many explanations online but I still don’t get it.

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First, I’ve never taken a physics class or attended highschool before, hence the ELI5. I’ve read many explanations but it doesn’t really make intuitive sense to me. For example (assuming there’s no air resistance / drag), let’s say I was traveling in a car going 120 mph and I wanted to decelerate to 90 mph. This would take four times as much energy than going from 30 mph to 0.

But let’s say there were two cars traveling at 120 mph. The car next to me decelerates to 90 mph, but I’m still going 120. From my point of view, the car next to me just started going 30 mph in the opposite direction. Why would this require 4 times as much energy than if both cars were just stationary, and the car next to me actually started going 30 mph in the opposite direction?

And, let’s say we’re both standing on earth. One person at the north pole and one at the equator. Both of us throw a ball, but the ball at the equator is already traveling at something like 1,000 mph due to the earth’s rotation. Shouldn’t throwing a ball eastward then require way more energy to go from 1,000 to say 1,020 mph, than the person throwing the ball at the north pole who just has to accelerate it from 0 mph to 20 mph?

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Anonymous 0 Comments

Simply because that is how it remains conserved.

Lets look at the conservation of momentum first. Its a vector quantity. We define momentum p=m×v that way because that is how it remains conserved. Now not only the direction but the “lenght” of that vector is conserved. We can create a scalar quantity based of of that fact. So just a number and call it kinetic energy.

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