Consider the rectilinear motion of a mass *m* being pushed by a constant force *F*, causing the mass’s speed to increase from *u* to *v* over a distance of Δ*s*.

Since a constant *F* results in constant acceleration *a*, we can apply the equation of motion.

But *ma* is *F*, so

Obviously, the quantity on the RHS represents the increase in kinetic energy of the mass.

The quantity on the LHS is given the name **work**. It is usually denoted by the symbol *W* and has the unit J.

This leads us to the work-energy theorem,

Recognize the resemblance with the impulse-momentum theorem

Basically, a force can change the KE and momentum of a body. If we multiply *F* with the Δ*s* of the body, we obtain the work done by the force, which can be equated to changes in the body’s KE. On the other hand, if we multiply *F* with Δ*t*, we obtain the impulse of the force, which can be equated to changes in the body’s momentum.

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**Demonstration**

Blow Pipe

**Concept Test**

0804

**Video Explanation**

Derivation of the KE Formula

Area Under the Force-Displacement Graph

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