Q:

Relativistic deceleration and energy

It's common knowledge that due to relativistic effects, accelerating from 0.8c to 0.9c takes a lot more energy than accelerating from 0.1c to 0.2c.
However, what's the case with deceleration? Does it take more or less energy when you are closer to the speed of light?
Due to the conservation of energy it should take the same amount of energy to accelerate from 0 to 0.9c in perfect vacuum than to decelerate from 0.9c to 0. However, is the distribution among the various velocities the same for deceleration and acceleration?

A:

The energy of a relativistic body is given by:
$$ E^2 = p^2c^2 + m^2c^4 $$
where $m$ is the rest mass and $p$ is the relativistic momentum, which is given by:
$$ p = \frac{mv}{1 - v^2/c^2} $$
Using this you can easily calculate the energy as a function of velocity. As you have already worked out, it doesn't make any difference whether you are accelerating or decelerating - the energy difference between any two velocities is always the same.

