Question

If the momentum of a body is numerically equal to its kinetic energy, what is the velocity of the body?

Answer 1

Let, m be the mass of the body and v be the velocity of the body.

Now, momentum of the body is

$p=mv$

Kinetic energy is

$E=\frac{1}{2}m{v}^2$

As per given condition

$\frac{1}{2}m{v}^2=mv=x\left(say\right)$

$\frac{1}{2}m{v}^2=x$

$\frac{1}{2m}{m}^2{v}^2=x$

$\frac{1}{2m}{x}^2=x$

$x=2m$

Now,

$mv=2m$

$v=2m{s}^{-1}$