Question

A 1300-kg car is skidding to a stop along a horizontal surface. The car decelerates from 27 m/s to a rest position in 4.5 seconds. Assuming negligible air resistance, determine the friction between the car tires and the road surface.

Answer 1

Given,

the mass of the car, m = 1300kg

initial velocity of the car, u = 27m/s

final velocity of the car, v = 0 m/s

time taken to come to rest, t = 4.5s

So, the acceleration(or deceleration) of the car, a = (v – u) / t = (0 – 27) / 4.5 = –6 m/s²

So, when the car is skidding to stop, the force on the car, is the kinetic(or sliding) friction(f_k) between the tires of the car and the surface, which is opposite to the direction of motion.

According to Newton's second law, –f_k= ma

–f_k = 1300x(–6)

–f_k = –7800 N

f_k = 7800 N

So, the friction between the car tires and the surface is 7800N, which brings the car to rest from 27m/s velocity, in 4.5s.