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# Power as force times velocity

Power $(P)$ is the work done (or energy generated) per unit time.

The work done is equal to the product of the force and the displacement in the direction of the force.

Remember also that the velocity is equal to the displacement per unit time.

Power is therefore: $$\Tblue{\text{power}} = \dfrac{\Tred{\text{force}} \times \Torange{\text{displacement}}}{\Torange{\text{time taken}}} = \Tred{\text{force}} \times \Torange{\text{velocity}}$$

A car travelling at $\Torange{30 \umps}$ faces a resistive force of $\Tred{ 100 \text{ N}}$. The power generated by the car's engine is $$\Tblue{P} = \Tred{100 \text{ N}} \times \Torange{30 \umps} = \Tblue{3000 \text{ W}}$$

Cyclists generates large amounts of power with their legs to travel at high velocities.