Question

A $150kg$ car engine develops $500W$ for each kg. What force does it exert to move the car at a speed of $20m{s}^{-1}$?

Answer 1

Step 1: Given data

$$\begin{gathered} Mass,\mathrm{m}=150\mathrm{kg} \\ Power,\mathrm{P}=500watt \\ Speed,\mathrm{u}=20\mathrm{m}/\mathrm{s} \end{gathered}$$

Step 2: Convert units

$$\begin{gathered} 1Watt=Joulse/second \\ 1kilowatt=1000watts=1000J/sec \end{gathered}$$

Step 3: Finding the Force

Power = Weight × Each power

$$\begin{gathered} =150\times 500 \\ =75000Watt \end{gathered}$$

The power in terms of force and speed is,

$$\begin{gathered} \mathrm{Power}=\mathrm{Force}\times \mathrm{Speed} \\ \mathrm{Force}=\frac{\mathrm{Power}}{\mathrm{Speed}} \\ \mathrm{F}=\frac{75000}{20} \\ \mathrm{F}=3750\mathrm{N} \end{gathered}$$

Hence, the force is $\mathbf{3750}\mathit{N}$.