# Nothing can exceed the speed of light but what if we accelerate a particle that contain electron that have a speed near to speed of light? [duplicate]

We all know that speed of light is $$3\times 10^8$$ $$\text{ }\mathrm{ms^{-1}}$$. The speed of electron inside the atom is $$2.7\times 10^8$$ $$\text{ }\mathrm{ms^{-1}}$$, which is close to speed of light.

So there is a machine that can accelerate the particle. Then when the particle move very fast, the resultant velocity of electron inside the particle should exceed the speed of light right?

In special relativity, velocities $$u$$ and $$v$$ are "summed" according to formula $$v_{\text{total}} = \frac{u+v}{1+\frac{uv}{c^2}}.$$ So, for example if $$u=v=c$$, we get $$v_{\text{total}} = \frac{u+v}{1+\frac{uv}{c^2}}= \frac{c+c}{1+\frac{c\cdot c}{c^2}}= \frac{2c}{1+1} =c$$ As you can see, you will always get a total velocity lower or equal to $$c$$.