 Sometimes people get a little bit confused with the idea that work is force times distance precisely because of this reason. If you sanity test it and you think I'll just hold this, I have to apply all this force, oh but I feel it's taking energy to hold something still and so distance doesn't seem to have anything to do with it. And the reason that's a kind of mistake is fairly clear if you put it down on a bench and you see the bench is now providing the force but the bench doesn't get tired. The bench isn't spending any energy at all. I could do that for a hundred years if I wanted to. And the reason we find so much difficulty holding it with our muscles is that our muscles are really inefficient and they're wasting all sorts of heat to just hold it there just from the way that they work. So while it's possible to waste energy in myriad ways, if you're actually applying a force to a particle then its energy will be changed by the force times the distance traveled. So a good example of that is to try and work out the stopping distance of a car. If a car is going at velocity v and you want to see how long it takes to stop one thing you could do is you could look at its acceleration another thing you could do is you could look at its kinetic energy. So you could say that the work done is going to have to equal its initial kinetic energy. To stop the car all the kinetic energy of the car has to be gotten rid of by the work done by the force of the wheels acting on the road. So the work done is going to be that force times the stopping distance and it's going to be equal to the kinetic energy which is a half m times the velocity of the car squared. So by rearranging we can see that the stopping distance is going to go up as the square of the velocity and inversely proportional to however good traction we have with our tyres. And that tells us why we have to leave more and more space to stop as we go faster and faster.