Answer:
The amount of gasoline is [tex]2.105\times10^{-2}\ gallons[/tex].
Explanation:
Given that,
Energy contained in gasoline [tex]= 1.3\times10^{8}\ J[/tex]
Mass = 2000 kg
Speed = 20 m/s
Energy used propel the car[tex] E=15\%\ of 1.3\times10^{8}\ J[/tex]
[tex]E=\dfrac{15}{100}\times1.3\times10^{8}[/tex]
[tex]E=19500000 = 1.9\times10^{7}\ J[/tex]
[tex]E=1.9\times10^{7}\ J[/tex]
We need to calculate the work done by the frictional force to stop the car
Using formula of work done
[tex]W=\Delta KE[/tex]
[tex]W=\dfrac{1}{2}m(v_{f}^2-v_{0}^2)[/tex]
[tex]W=\dfrac{1}{2}\times2000\times(0-20^2)[/tex]
[tex]W=-4.0\times10^{5}\ J[/tex]
Therefore,
Work done to bring the car back to its original speed
[tex]W=4.0\times10^{5}\ J[/tex]
[tex]Amount\ of\ gasoline\ needed = \dfrac{W}{E}[/tex]
[tex]Amount\ of\ gasoline =\dfrac{4.0\times10^{5}}{1.9\times10^{7}}[/tex]
[tex]Amount\ of\ gasoline =2.105\times10^{-2}\ gallons[/tex]
Hence, The amount of gasoline is [tex]2.105\times10^{-2}\ gallons[/tex].
