A car weighing 500 kg moves at a speed of 20 m / s. How far will the car travel when the brakes are fully applied?

A car weighing 500 kg moves at a speed of 20 m / s. How far will the car travel when the brakes are fully applied? The coefficient of sliding friction of wheels on the asphalt is 0.4, the acceleration of gravity is considered equal to 9.8 m / s2.

Let us find the resultant of the forces acting on a car with a mass of m = 500 kg, moving at a speed of vо = 20 m / s, according to Newton’s second law: ma = – F friction. Since the car moves with the brakes fully pressed, the friction force is found through the reaction force of the support N = mg; F friction = µ • N = µ • mg. The coefficient of sliding friction of wheels on the asphalt is µ = 0.4, the acceleration of gravity g = 9.8 m / s ^ 2; ma = – µ • mg; a = – µ • g; a = – 0.4 • 9.8 m / s ^ 2; a = – 3.92 m / s ^ 2.
In order to determine which way the car will go to the stop v = 0 m / s, we will use the formula of the path for uniformly slowed motion: S = (v ^ 2 – vо ^ 2) / 2а; then S = ((20 m / s) ^ 2) / (2 (- 3.92 m / s ^ 2)). S = 51.02 m.
Answer: when braking S = 51.02 m.