Question

A body of mass m is moving with a velocity v. Write the expression for its kinetic energy.

Answer 1

Assume that a mass-m body is travelling at a velocity of v. An opposing force, F brings it to rest.

Let a represent the force's uniform retardation, and let it travel a distance of S before coming to rest at T. Then,

The kinetic energy of the body = the work done by the retarding force in stopping it.

Kinetic energy = Force × displacement

= F × S  ...(i)

Retarding force F = ma  ...(ii)

Initial velocity u = v, final velocity v = 0

From the relation v² = u² +2aS

0 = v² - 2aS (since a is the retardation)

∴ Displacement S = `v^2/(2a)`  ...(iii)

Substituting the values of F and S from equation (ii) and (iii) in equation (i), we get

kinetic energy `K = F × S = ma × v^2/(2a) = 1/2 mv^2`

Kinetic energy = `1/2 ` mass × (velocity)²