Power

Power is the rate of which a force does work on a body. $$\text{Power} = \frac{\text{Work done}}{\text{time}}$$ Using $w=Fd$ the formula for power becomes $$\begin{align} P &= \frac{Fd}{s}\\ P &= Fv \end{align}$$

Example

Given the body has a mass of $660\text{ kg}$ and the power of the system is $16\text{ kW}$ what is the vehicles maximum speed.

Find $F$

$$\begin{align} F &= ma\\ F - 660g\sin(17^{\circ}) - 140 &= 660 \times 0\\ F &= 2031\text{ N}\\ \end{align}$$

Find $v$

$$\begin{align} 16000 &= 2031 \times v\\ v &= 7.878\\ &= 7.88\text{ ms}^{-1} \end{align}$$