Can $p=mv$ be used for speeds close to $c$?

Question

Can I use the formula $p=mv$ for a particle which is travelling at a speed which is very close to the speed of light?

Answer 1

No you can't. You need to use $p = \gamma m v$ where $m$ is the rest mass.

For reference: https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation

Answer 2

No, you can't.

Instead you need to use the relativistic momentum $$p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}$$ where $m$ is the invariant mass (formerly also called rest mass).

You see, that this formula will result in $p\to\infty$ when $v\to c$.

Answer 3

Yes, but m is the relativistic mass. In terms of the rest mass $m_0$, $m = m_0/\sqrt{1 - {v^2/c^2}}$.