Question

A car of mass 'm ' is driven with acceleration 'a' along a straight level against a constant external resistive force 'R' .When the velocity of the car is 'V' ,then prove that the rate at which the engine of the car is doing work is (R + ma)V.

Answer 1

$$\begin{gathered} FromNewton\text{'}ssecondlaw: \\ {F}_{net}=ma \\ F-R=ma \\ F=R+ma \\ WhereFisappliedforceandRisresistiveforce. \\ \mathit{R}\mathit{a}\mathit{t}\mathit{e}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{d}\mathit{o}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{w}\mathit{o}\mathit{r}\mathit{k}\mathbf{}\mathbf{\left(}\mathit{o}\mathit{r}\mathbf{\right)}\mathbf{}\mathit{P}\mathit{o}\mathit{w}\mathit{e}\mathit{r}\mathbf{:} \\ P=\frac{W}{t} \\ =FV \\ \mathbf{}\mathbf{=}\left(\mathbf{R}\mathbf{+}\mathbf{m}\mathbf{a}\right)\mathit{V} \end{gathered}$$