Respuesta :
We know that the work is related to the kinetic energy by the work energy theorem:
[tex]W=K_f-K_i[/tex]In this case the final velocity of the car is 0 m/s; with this in mind and plugging the values given for the initial velocty we have:
[tex]\begin{gathered} W=\frac{1}{2}(1180)(0)^2-\frac{1}{2}(1180)(18.2)^2 \\ W=-195431.6 \end{gathered}[/tex]Now, we know that the work is given by:
[tex]W=Fd[/tex]plugging the distance and the work done we have:
[tex]\begin{gathered} -195431.6=0.411F \\ F=-\frac{195231.6}{0.411} \\ F=-4.76\times10^5 \end{gathered}[/tex]Since we need the magnitude we drop the sign, therefore the magnitude of the force is:
[tex]F=4.76\times10^5\text{ N}[/tex]