Question

Derive an expression of kinetic energy of mass in movin with velocitu

Answer 1

Let a body of mass ‘m’ is moving with a velocity ‘v’.A force ‘F’ is applied on it to stop its motion for which the retardation ‘h’ is produce in the body and the body covers a distance ‘s’ before coming rest.

Work done by the force to stop the motion of the body is the measure of kinetic energy .

Here

Initial velocity = v

Final velocity = 0(zero)

From Newton’s 2nd law

F = ma

or, a = F/m

From 3rd equation of motion

0=v^2 - 2as

or, 2as = v^2

or, 2 × F/m × s = v^2

or, s = (mv^2) /2F

Therefore , workdone by the force,

W = Fs

or, W = F ( mv^2 )/2F

or, W = 1/2 mv^2

Hence,

Kinetic energy = 1/2mv^2.

Answer 2

Let a body of mass ‘m’ is moving with a velocity ‘v’.A force ‘F’ is applied on it to stop its motion for which the retardation ‘h’ is produce in the body and the body covers a distance ‘s’ before coming rest.

Work done by the force to stop the motion of the body is the measure of kinetic energy .

Here

Initial velocity = v

Final velocity = 0(zero)

From Newton’s 2nd law

F = ma

or, a = F/m

From 3rd equation of motion

0=v^2 - 2as

or, 2as = v^2

or, 2 × F/m × s = v^2

or, s = (mv^2) /2F

Therefore , workdone by the force,

W = Fs

or, W = F ( mv^2 )/2F

or, W = 1/2 mv^2

Hence,

Kinetic energy = 1/2mv^2.