Question

At what speed is the particle moving, if its mass is equal to four times its rest mass?

Answer 1

OHH

Bro : Seems like you are now entering me into the Relativistic Mechanics.(Cool...)

Here, Principles of Classical Mechanics :---
Blah ....Blah ... will not work here.


Since, you are talking about relationship about masses with their speed.

Or Changing the mass .

Recall Einsteins Special Relativity:

I'm assuming the particle is moving with
constant speed otherwise Einsteins General Relativity will work here.



According to your question ,
=> Lorentz factor is 4.
=>
$\frac{1}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } = 4 \\ \frac{ {v}^{2} }{ {c}^{2} } = \frac{15}{16} \\ v \: \: = \frac{ \sqrt{15} }{4} c \\ where \: c \: is \: the \: speed \: of \: light.$

So, Finally we can say that speed (constant ) is constant here.


::::Danger$$$$$$::::

Above speed will not work here if particle is accelerated.




Hope, you get my answer and understandable to you.