Question

Nick is driving his car on a straight country road with a coefficient of friction between the tires and the road of 0.45. A moose jumps on to the road in front of his view and he immediately slams on the brakes, leaving a skid mark that is 250 feet long before coming to a stop. A policeman who minored in physics sees your car stopped on the road, looks at the skid mark, and gives you a ticket for traveling over the 60 mph speed limit. Should you fight the ticket in court?

Answer 1

first the work done by friction to stop the car needs to be obtained , and from it calculate the speed

The change in the cars kinetic energy is equal to the work done by the frictional force to stop the car.

Therefore

$\Delta k= -f_k$

$-(\frac{1}{2}mv_i^{2}-\frac{1}{2}mv_f^{2})= -\mu mgd$

now making the initial velocity subject of the formula

$v_i= \sqrt {2(\mu gd+\frac{1}{2}}v_f^{2})$

substituting the given values $\mu= 0.45$ , $g=9.8m/s^{2}$ ,$d=250 ft\space or\space 76.2m$,$v_f^{2}=0m/s$ in the equation

$v_i=\sqrt{2(0.45\times9.8\times76.2)+0}$

$v_i=25.9m/s\space or\space 57.98mph$

This is the speed Nick was travelling at before he hit the brakes, therefore he should fight the ticket in court since he had not exceeded the 60 mph limit