Question

prove kinetic formula​

Answer 1

PROVE:-

Suppose a Body of mass "m" moving with Initial Velocity "u". let it now be displaced through a distance "s" when a Constant unbalanced force "f" act on it in the direction of its Displacement. The work is done - F × s. It will cause a change in it's Velocity. Let its Velocity change from u to v. Let a be the Acceleration Produced.

We have read newton's third Equation of motion

i.e - v² - u² = 2as

This give,

→ s = v² - u² / 2a.....1

We know F = ma Thus , Putting it in eq. 1. we can write work done by the force F is

→ w = ma

→ w = ma ( v² - u²)/ 2a

→ w = m × (v² - u²)/2

→ w = ½ × m × v² - u²

But, The object was at rest. So, u = 0.....2

From 2 we get

→ w = ½ × mv²

Therefore,

The Kinetic Energy Posses by body moving with Uniform Velocity is given as

→ K. E = ½ × mv²

PROVED√√√