Question

a moving car encounters air resistance which is prortional to the sqaure of speed of the car . The ratio of power required at 40 km/h to that required at 80 km/h, to move at constant speed

Answer 1

$$\begin{gathered} \mathbf{Power}\mathbf{}\mathbf{is}\mathbf{}\mathbf{proportional}\mathbf{}\mathbf{to}\mathbf{}\mathbf{the}\mathbf{}\mathbf{square}\mathbf{}\mathbf{of}\mathbf{}\mathbf{speed}\mathbf{:} \\ \mathrm{P}\mathrm{\alpha }{\mathrm{v}}^2 \\ \frac{{\mathrm{P}}_1}{{\mathrm{P}}_2}={\left(\frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}\right)}^2 \\ ={\left(\frac{40}{80}\right)}^2 \\ =\frac{\mathbf{1}}{\mathbf{4}} \end{gathered}$$