# Kinetic Energy Equation/Simple Explanation?

1. Sep 1, 2011

### agentsanta

Ok, so I sort of have an idea of what kinetic energy is but I'm still kind of confused. I'm confused mainly because of the equation. Every source I've gone to has just given me the equation
EK=1/2mv^2
but none of the sources mentions where it came from or what it means
It almost seems like someone just pulled it out of thin air
Could someone give me a simple yet effective explanation of what Kinetic Energy is and the meaning/derivation of that formula?

2. Sep 1, 2011

### SteamKing

Staff Emeritus
3. Sep 2, 2011

### Staff: Mentor

KE is the amount of work required to get an object from rest to its current speed.

4. Sep 2, 2011

### Hootenanny

Staff Emeritus
In the absence of friction or other dissipative forces. In other words, it is the amount of work done on an object moving at speed v, with mass m.

5. Sep 2, 2011

### Staff: Mentor

Good point, thanks for the clarification.

6. Sep 2, 2011

### Hootenanny

Staff Emeritus
Just to make sure: I wasn't correcting or providing clarification for you , I wouldn't dream of doing that.

7. Sep 2, 2011

### Lsos

It's pretty straight forward if you think about it.

The m is mass...obviously a train, being more massive, will have more energy than a car travelling at the same speed.

The v is velocity. Again, obviously a faster moving car will have more energy than a slower moving car. If it hits a wall, it will get more deformed, it takes longer to stop, etc.

The velocity is squared because it's much harder to accelerate a car to 40mph than to 20mph. 4x harder, to be precise.

Might not make sense at first, but if you jump out of a 2nd floor window you will NOT hit the ground twice as fast as from a 1st floor window (assuming the 2nd floor is 2x higher than the 1st). It's because the higher you jump, the faster you go and the less time gravity has to pull you down. You actually have to jump from the 4th floor in order to let gravity pull on you twice as long, and to hit the ground twice as fast (and 4x harder). Don't jump out of windows, but you can drop stuff down to convince yourself of this.

Works the same with cars and everything else...you need to accelerate through 4x the distance to go 2x as fast. Braking, too...you need 4x more road to brake from 100mph as from 50mph.

I don't know what's up with the 1/2 mv^2. Either way, the point remains that energy is proportional to how much mass you have, and exponentially proportional to how fast you're going. That's all the equation is saying. It by no means is pulled out of thin air.

8. Sep 2, 2011

### chrisbaird

Or equivalently, the amount of work required to completely stop an object that is moving as some speed. Think about trying to stop a shopping cart coming at you by holding out your hand. If the speed is greatly, the cart has more kinetic energy, and you will have to do more work to stop it. If its mass is greater (it's filled with watermelons), again, it will have more kinetic energy and will require more work to stop.

9. Sep 2, 2011

### agentsanta

Sorry for the late reply I was a little busy
Thx for all the replies, I get it now