# Why is kinetic energy calculated using speed?

Why is kinetic energy calculated using speed? Since speed is distanced covered, and if a car moves 100 meters around a circular track -- stoping after moving half of the distance of the track -- the car wouldn't have as much kinetic energy because it doesn't displace as much as it covers. But surely the car has kinetic energy as it moves, right? It covers more distance than it changes position. So shouldn't it have more kinetic energy because it moves more than it changes position? Is there a reason kinetic energy is calculated using speed?

Please don't use any math beyond 8th grade; I haven't learned past it yet.

• Kinetic energy is not calculated using velocities, it is rather defined so. As for all definitions, there is no correct or incorrect way, they are just names given to quantities. However, why the expression $1/2\,mv^2$ enters the equations is another topic and you can see that it relates to the work done by the force along a path. – gented Oct 10 '15 at 19:58

At the level of an introductory course energy is defined as a property of an object or system that allows it to do work (there are some subtleties to that definition, but it is a place to start), and kinetic energy is an easy example: a moving baseball could drive a nail some distance into a wall if it hit it head on, and how far it would be able to drive it depends on how fast it was moving in a quadratic manner (assuming constant resistance).

That ability is a feature of it's speed that does not depend on the direction of motion (aside from the need to put the hypothetical nail in a different place), so the quantity kinetic energy should not depend on the direction of motion.

Kinetic energy is a thing you have, just like an instantaneous position or an instantaneous speed or an instantaneous velocity.

And it can change from moment to moment just like those other things.

You seem to think kinetic energy is related to average velocity (displacement during a time interval over duration of said same time interval), it is not. Firstly, if it were, then kinetic energy would be defined over an interval, but it actually exists at every moment. Secondly, that just isn't the definition of kinetic energy, the definition requires the instantaneous velocity or instantaneous speed.

If you choose a really tiny time interval, the average velocity of that tiny time interval will start to get really close to the instantaneous velocity, but that's basically the case when the time interval is small enough that you basically move in an approximately straight line at an approximately steady speed.

The formula for kinetic energy is

$$T = \frac{1}{2}mv^2$$

When we measure the kinetic energy. we use the instantaneous speed i.e the speed at that particular moment e.g the speed that your speedometer on the car measures is not the average speed but the instantaneous speed. If you take the average speed into account, you won't get the value of the kinetic energy at the particular instant as kinetic energy is defined for instantaneous velocity not average velocity. The average velocity in this case would be zero as the net displacement is zero.