Explanation:
Given, the mass of the car [tex]m=1430\textrm{ }kg[/tex]. The car speeds up from [tex]7.50\textrm{ }\frac{m}{s}\textrm{ to }11.0\textrm{ }\frac{m}{s}\textrm{ in }9.30\textrm{ s.}[/tex].
Since friction is assumed zero, it is clear that all the work done by the forces responsible is going into increasing the speed of the car.
[tex]\textrm{ Average Power = }\frac{\textrm{Total Work done}}{\textrm{Time taken}}[/tex]
[tex]\textrm{Work done = Change in Kinetic Energy}[/tex]
[tex]\textrm{Work done = }[/tex]Δ[tex]\textrm{ KE = }\frac{1}{2}mv_{f}^{2}-\frac{1}{2}mv_{i}^{2}[/tex]
[tex]\textrm{Work done = }\frac{1}{2}(1430kg)(11.0\frac{m}{s})^{2}-\frac{1}{2}(1430kg)(7.50 \frac{m}{s})^{2}[/tex][tex]\textrm{ = }46,296.25J[/tex]
[tex]\textrm{Average Power = }\frac{46296.25J}{9.30s}=4978.09W=4.978kW[/tex]
∴ Power required = [tex]4.978kW[/tex]
