# Chapter 26 - Conceptual Questions - Page 1008: 10

A particle with mass cannot move faster than the speed of light.

#### Work Step by Step

We can write an expression for the relativistic mass of an object when it is moving at speed $v$: $m_{rel} = \frac{m}{\sqrt{1-\frac{v^2}{c^2}}}$ We can write an expression for the kinetic energy: $K = \frac{1}{2}~m_{rel}~v^2$ We can see that as $v$ gets closer to $c$, the value of $m_{rel}$ increases without any upper limit. A particle would require infinite energy to travel at the speed of light, which is clearly impossible. Therefore, a particle with mass cannot move faster than the speed of light.

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