Question

A body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity changes from u to v. How much work is being done by the force?

Answer 1

The body of mass m is moving with a uniform velocity u.

A force is applied on the body due to which its velocity changes from u to v and produces an acceleration a in moving a distance S.

Then, Work done by the force = force × displacement

W = F × S    ...(i)

From relation : v² = u² + 2 a S

Displacement, S =`(v^2-u^2)/(2a)`

And force, F = ma

From equation (i), W = `ma xx ((v^2-u^2)/(2a))` 

=`1/2m(v^2-u^2)`

= K₁ - K₂

Where K₁ is the initial kinetic energy = `1/2 mv^2`

And K₂ is the final kinetic energy = `1/2 mv^2`

Thus, work done on the body = Increase in kinetic energy

W = `1/2 m(v^2 - u^2)`