# Varying of momentum for constant kinetic energy

How is that If the momentum of the particle is constant with time, its kinetic energy ($$E_k$$) should also be constant with time a true statement but the converse is false...

When momentum is constant,

$$\begin{eqnarray} p&=&mv \\ E_k=(mv^2)/2& =& (mv)^2/2m\\ E_k&=&p^2/2m\\ \end{eqnarray}$$ therefore when $$p$$ is constant, $$m$$ is a constant. So $$E_k$$ is also constant...

Isn't it same the other way as well.....when $$E_k$$ is constant, $$m$$ anyway a constant therefore $$p^2$$ is a constant which makes $$p$$ a constant?

But my note says that when $$E_k$$ is constant with time, $$p$$ should also be constant with time is false......so how will the momentum ($$p$$) vary?

• NOTE, The opposite of the statement "If A then B" is "If A then NOT B". The statement "If B then A" is the converse of the first, not the opposite. – definitelynotbs Jul 13 '19 at 10:47
• Edited it...thank u – user687961 Jul 13 '19 at 11:02