Police investigators are trying to prove that a motorist exceeded the speed limi
ID: 1704493 • Letter: P
Question
Police investigators are trying to prove that a motorist exceeded the speed limit (55mi/hr=24.6 m/s) based on a 72-m-long skid marks made as the motorist came to a stop at a red light. It is known that the coefficient of kinetic friction between rubber and the pavement is about 0.80.a. Draw a picture of the scenario. Indicate your system and coordinate axes on this picture.
b. Draw a free-body force diagram
c. Apply Newton's 2nd Law and find the acceleration of the car
d. Should the motorist be ticketed? Why? Show your evidence.
Explanation / Answer
d=-72m
Myu=0.8
N = Normal Force = M*g
M = Mass
a = Acceleration
F=Myu*N=Myu*M*g=M*a
Myu*g=a
a=-9.81*0.8
a=-7.848m/s^2
V(final)^2 = V(initial)^2 + 2*a*d
V(final)=0
0=V(initial)^2 + 2*a*d
V(initial)^2 = 2*a*d
V(initial)= sqrt( 2*a*d)
V(initial)= sqrt(2*-7.848*-72)
V(initial)=|33.6m/s|
Remember that the acceleration of the car is negative in this coordinate system. The Motorist should be ticketed - Over the speed limit.