# Work done by force applied for an instant

We know $${\rm work} = \int F \cdot dl$$ , where $$dl$$ is the displacement of point of application of force.

Suppose I apply an instant force of $$100~\rm N$$ on a body and then remove the force; after that the body moves a distance $$d$$. When the body is moving there is no external force (other than friction, $$mg$$, normal reaction force). So what is the work done by $$100~\rm N$$ force?

Is is zero? Because when the body moved distance $$d$$, the $$100~\rm N$$ force was not there.

• If we draw a free body diagram while the body is moving, there will be only forces like mg, normal,air drag and no external force, so where is the work done by that force??I am just confused a lot Jun 9, 2018 at 6:38
• In the formula $W=\vec{F} . \vec{l}$ , $l$ is zero , cause it is the distance traversed as long as $F$ acts ... Jun 9, 2018 at 8:28
• Thanks , thats a perfect reply.dl should be calculated as long as F acts. Jun 9, 2018 at 8:49

$d=0$ in your example, because the work is zero and so the kinetic energy of the body is zero. A finite force applied for an instant doesn't do any work.
• It's $1000 J$ work ... Jun 9, 2018 at 9:37