Question

A $1.0g$ particle has momentum $400,000kgm/s$. What is the particle’s speed in m/s?

Short answer

$400m/s$

Step-by-step solution

Given Information

We have given that a $1.0g$particle has momentum $400,000kgm/s$.

We have to find the particle’s speed in $m/s$.

Simplify

The momentum in relativity is given by

$P=\frac{mv}{\sqrt{1-{\displaystyle \frac{v^2}{C^2}}}}$

Here

$P=400,000kgm/s$and

$$\begin{gathered} m=1g \\ =1\times {10}^{-3}kg \end{gathered}$$

So, the equation becomes

$$\begin{gathered} 400,000=\frac{1\times {10}^{-3}\times v}{\sqrt{1-{\displaystyle \frac{v^2}{{(3\times {10}^8)}^2}}}} \\ v=400m/s \end{gathered}$$