Question #127331

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?

Expert's answer

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

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