# Energy Needed To Go A Given Speed

1. Jun 18, 2011

### Sothh

Hey, I don't have much of a physics background.

I have been searching for an equation that shows how much energy is needed to make a given mass go a given speed.

For example, lets say I want to send 1 gram at half light speed. How much energy is required?

Thanks!

2. Jun 18, 2011

### Staff: Mentor

Sounds like you want to calculate the kinetic energy of the mass.

For low speeds (compared to the speed of light) the kinetic energy is KE = ½mv². But for fast speeds, it's a bit more complicated:

(I can't seem to get Latex to work.)

3. Jun 18, 2011

### tiny-tim

Welcome to PF!

Hi Sothh! Welcome to PF!

For a speed of v metres per second, the energy of a mass of m kilograms is mc2/√(1 - v2/c2) joules.

If v = 0 (the mass is at rest), that energy is obviously just mc2, which is therefore called the rest-mass.

So the extra energy needed to get it to speed v (the kinetic energy) is mc2(1/√(1 - v2/c2) - 1) joules.

If v/c is very small, then that extra (kinetic) energy is approximately mc2(v2/2c2), ie mv2/2.

4. Jun 18, 2011

### Sothh

Thanks!

Just to confirm I am using this correctly, it should take 20 kilograms around 9e+12 kilojoules to go .1c, correct?

5. Jun 18, 2011