## Quick Reference

The work done by a force **F** during the time interval from *t*=*t*_{1} to *t*=*t*_{2} is equal towhere **v** is the velocity of the point of application of **F**.

From the equation of motion *m***a**=**F** for a particle of mass *m* moving with acceleration **a**, it follows that *m***a**. **v**=**F**. **v**, and this then gives (*d/dt*)(½*m***v.v**)= **F.V.** By integration, it follows that the change in kinetic energy is equal to the work done by the force.

Suppose that a particle, moving along the *x*-axis in the positive direction, with displacement *x*(*t*)**i** and velocity *v*(*t*)**i** at time *t*, is acted on by a constant force *F***i** in the same direction. Then the work done by this constant force during the time interval from *t*=*t*_{1} to *t*=*t*_{2} is equal towhich equals *F*(*x*(*t*_{2})−*x*(*t*_{1}). This is usually interpreted as ‘work=force×distance’.

The work done against a force **F** should be interpreted as the work done by an applied force equal and opposite to **F**. When the force is conservative, this is equal to the change in potential energy. When a person lifts an object of mass *m* from ground level to a height *z* above the ground, work is done against the uniform gravitational force and the work done equals the increase *mgz* in potential energy.

Work has the dimensions ML^{2} T^{−2}, the same as energy, and the SI unit of measurement is the joule.

*Subjects:*
Mathematics.

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