# Can you replace c with velocity in #E = mc^2#?

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If the question is about the energy of a neutron moving at a certain fraction of the speed of light. mass of neutron is given.

If the question is about the energy of a neutron moving at a certain fraction of the speed of light. mass of neutron is given.

##### 1 Answer

see below

#### Explanation:

It really depends upon what you mean by "certain fraction".

Generalising that, the **relativistic** expressions for energy and momentum of a **free** particle moving in 1-D are:

- With
**rest**energy:#qquad E_o = m_o c^2#

So the additional energy in the rest frame of a relativistic free particle due to its motion can be explored as:

- From
#square# :#qquad v^2 = p^2/(gamma^2 m_o^2)#

Therefore:

In the real world, we work with the blue term