Question

If the linear momentum of a particle is known, can you find its kinetic energy? If the kinetic energy of a particle is know can you find its linear momentum?

Answer 1

Yes, the kinetic energy of the particle can be determined if the value of linear momentum is known.
The kinetic energy is calculated using the formula:
$$\begin{gathered} \mathrm{K}.\mathrm{E}=\frac{1}{2}m{v}^2=\frac{p^2}{2m} \\ w\mathrm{here},p\mathit{}\mathrm{is}\mathrm{the}\mathrm{linear}\mathrm{momemtum}\mathrm{having}\mathrm{value}mv. \end{gathered}$$

But linear momentum cannot be determined even if the kinetic energy is known because linear momentum is a vector quantity, whereas kinetic energy is a scalar quantity. Thus, the direction of the linear momentum remains unknown, however its magnitude can be calculated.