# Relativistic energy equations

1. Apr 22, 2010

### jaketodd

Are Einstein's energy equations for relativistic speeds linear? For example, if you had something going at relativistic speed and then slowed it, but still had it at relativistic speed, would the decrease in energy be directly proportional to the amount you slowed the thing down?

Thanks,

Jake

2. Apr 22, 2010

### Staff: Mentor

Relativistic energy:

$$E = \frac{m_0 c^2}{\sqrt{1 - v^2 / c^2}}$$

Work out an example or two for yourself, and see what you get.

3. Apr 22, 2010

### yuiop

You can also use:

$$E = \sqrt{(m_0 c^2)^2 - \frac{(m_0 v c)^2}{(1-v^2/c^2)}} = \sqrt{(m_0 c^2)^2 - (p c)^2}$$

Where p = relativistic momentum. This form has the advantage that it can be used for particles with zero rest mass like photons.

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