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Home » A body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity increases from u to v. How much work is being done by the force?
A body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity increases from u to v. How much work is being done by the force?
Class 10 | ICSE | Physics | Selina | Work Energy
A body of mass m is moving with a uniform velocity u. A force is applied on the body due to which its velocity increases from u to v. How much work is being done by the force?

Solutions:

Allow a mass m to move at an initial velocity u. When force is applied to the body in its motion direction, an acceleration ‘a’ is produced, and the body’s velocity changes from u to v while moving a distance S. So,

We know that the work done by the force = force × displacement

W = F × S             ———– (1)

From the relation

v2 = u2 + 2aS, we have –

From which displacement can be calculated as follows –

 S = (v2 – u2) / 2a

We know that Force, F = ma

Substituting the values of F and S in equation (1), we obtain –

W = F × S = ma × (v2 – u2) / 2a

= 1 / 2 mv2 – 1 / 2 mu2

Or, we can write W = kf – ki

Hence, it can be concluded that the work done on the body is equal to the increase in kinetic energy.

Therefore, W = 1 / 2 m (v2 – u2)

i

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