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maina89 · May 4, 2010, 10:31 AM

Hello!
If 2 objects have the same mass and one of them is moving with a speed that is twice the speed of the other. Wich way can I find the relation between their works

ebaines · May 4, 2010, 11:10 AM

The two masses have kinetic energy due to their mass and velocity. The formula for kinetic energy is:

$<br /> KE = \frac 1 2 m v^2<br />$

So you can see that if two objects have the same mass, but one is moving at twice the velocity of the other, it has four times the kinetic energy.

Now, energy is related to work in that to get the mass up to a given level of KE from rest something had to do work on the object. The amount of work that was performed is equal to the gain in KE of the object - thus if it takes a certain amount of work to accelerate an object from rest to a particular velociity, it takes four times as much work to accelerate that object from rest to twice the velocity. Same thing in reverse - it takes four times as much work to stop an object if it is going twice as fast as another object of the same mass. This is why to stop your car with your brakes it takes four times the distance of road when you're trying to stop from 60 MPH than it does if it you are only going 30 MPH.