Traffic police examine the scene of an accedient involving two cars and measure a 72 metre long skid mark of one of the cars, which nearly came to stop before colliding.The accdient occured on a section of highway that had a 100 kilometre per hour speed limit. The coefficient of kinetic friction between rubber from tyres and the pavement is about 0.80. The driver of the vehicle that created the long skid marks claims to have been travelling at less than 100 kilometre per hour. Is he telling the truth?

Question

Traffic police examine the scene of an accedient involving two cars and measure a 72 metre long skid mark of one of the cars, which nearly came to stop before colliding.The accdient occured on a section of highway that had a 100 kilometre per hour speed  limit. The coefficient of kinetic friction between rubber from tyres and the pavement is about 0.80. The driver of the vehicle that created the long skid marks claims to have been travelling at less than 100 kilometre per hour. Is he telling the truth?

henry2, · Answer

Fc = M*g = 9.8M = force of the car = Normal force(Fn).
Ff = u*Fn = 0.8*9.8M = 7.84M = force of kinetic friction.
Fp = Mg*sinA = mg*sin 0 = 0 = Force parallel with the plane.

Fp-Ff = M*a.
0 - 7.84M = M*a,
divide both sides by M:
a = -7.84 m/s^2.

Vo = 100km/h = 100,000m/3600s = 27.78 m/s.
V^2 = Vo^2 + 2a*d = 0.
27.78^2 + (-15.7)d = 0,
d = 49 m = stopping distance when driving 100km/h.
The driver who created the 72-meter skid marks was driving above the speed limit.