# Energy Needed to Maintain Velocity

1. Oct 27, 2009

### Riceman1974

I know how to figure out how much energy is needed to acclerate to a certain speed. What I don't know is how much energy is needed to maintain that speed.

For example. I was watching the first Trek movie the other day, and Kirk orders the Enterprise to go to .5 light speed. So the Enterperise goes from 0 to 150M meters per second in like 5 seconds. I wondered how much force would be needed to do that, so I calculated:

F = M * A
The ship has a mass of 200,000 metric tons, so 200,000,000 kg * acceleration, which going from 0 to .5 light in 5 seconds would be 30,000,000 meters per second per second (i hope that's right).

That gave me 6*10^15 Newtons (damn!)

I then tried to see what this would be in joules, so I next calculated the distance traveled, using:

Distance = .5*Acceleration*Time^2
.5*30,000,000*(5^2)

That gave me 375,000,000 meters.

To then calculate joules, I used W(joules) = Force * Distance
6*10^15 * 375,000,000

That gave me 2.25*10^24 joules of energy needed to accelerate a 200,000 metric ton object to .5 light speed in 5 seconds (please correct me if I'm wrong).

My question, how many joules per second is needed to maintain that speed?

This is not homework. I'm just a nerd.

2. Oct 27, 2009

### PatPwnt

0 Joules/sec are necessary, if you are traveling in a vacuum(space) see newtons first law. Also, the energy required to get up the speed is a little more than you calculated because when you increase your speed, your mass increases as well, see special relativity / einstein. But, your method of calculations are right if you ignore special relativity ( I didnt actually do your calculations). You don't need to calculate the energy from force times d, you can use 1/2 m v^2 too. (would have been quicker, but same answer.)