Question

Traveling at a speed of 15.8 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the road is 0.540. What is the speed of the automobile after 1.19 s have elapsed? Ignore the effects of air resistance.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the automobile = M

Normal force on the automobile from the road = N

N = Mg

Coefficient of kinetic friction between the tires and the road = = 0.54

Friction force on the automobile = f

f = -N (Negative as the friction force will be acting in the opposite direction of the motion of the automobile)

f = -Mg

Acceleration of the automobile = a

Ma = f

Ma = -Mg

a = -g

a = -(0.54)(9.81)

a = -5.3 m/s²

Initial speed of the automobile = V₁ = 15.8 m/s

Speed of the automobile after 1.19 sec = V₂

Time period = T = 1.19 sec

V₂ = V₁ + aT

V₂ = 15.8 + (-5.3)(1.19)

V₂ = 9.49 m/s

Speed of the automobile after 1.19 sec = 9.49 m/s