Question

Prove that kinetic energy =p2/2m

Answer 1

hello....!!

E and p are kinetic energy and the momentum of the body.

PE = Mv
E= 1/2 Mv^2
E = 1/2 Mv^2 * M/M
E = 1/2 (Mv)^2/M
E = p^2/2M

Relation between the K.E. & Momentum of body

hope this helps you

Answer 2

Explanation:

The energy possessed by an object due to its motion is called its kinetic energy.

It is given by :

$E=\dfrac{1}{2}mv^2$...... (1)

We know that the momentum of an object is given by,

p = m × v

Multiply and divide both sides of equation (1) by m as

$E=\dfrac{1}{2}mv^2\times \dfrac{m} {m}$

$E=\dfrac{1}{2}(mv)^2\times \dfrac{1} {m}$

So, the above equation can be rearranged as :

$E=\dfrac{p^2}{2m}$

Hence proved.