Question

4. A particle of mass in moves with momentumn of magnitude p.

(A) Show that the kinetic energy of the particle is KE = (P ^ 2)/(2m)

(B) Express the magnitude of the participle's momentum in terms of its kinetic energy and mass.

Answer 1

The momentum of the particle by dfinition

$$p=mv$$

(A) The kinetic energy

$$E_k=\frac{mv^2}{2}=\frac{m(p/m)^2}{2}=\frac{p^2}{2m}$$

(B)

$$p=\sqrt{2mE_k}$$