We are asked to determine the force required to stop a car that is moving at a velocity of 91.3 km/h.
First, we will convert the 91.3 km/h into m/s. To do that we will use the following conversion factors:
[tex]\begin{gathered} 1km=1000m \\ 1h=3600s \end{gathered}[/tex]Multiplying the conversion factors we get:
[tex]91.3\frac{km}{h}\times\frac{1000m}{1km}\times\frac{1h}{3600s}=25.36\frac{m}{s}[/tex]Now. We use a balance of energy. The work done by the force to stop the car must be equal to the change in kinetic energy of the car, therefore, we have:
[tex]W=\frac{1}{2}mv_f^2-\frac{1}{2}mv_0^2[/tex]Since the car will stop this means that the final velocity is 0:
[tex]W=-\frac{1}{2}mv_0^2[/tex]The work done is equal to the product of the force and the distance:
[tex]Fd=-\frac{1}{2}mv_0^2[/tex]Now, we divide both sides by the distance "d":
[tex]F=-\frac{mv_0^2}{2d}[/tex]Substituting the values:
[tex]F=-\frac{(1070kg)(25.36\frac{m}{s})}{2(128m)}[/tex]Solving the operations:
[tex]F=-106N[/tex]Therefore, the magnitude of the force required is 106 Newtons.
