A car moving at a speed of 60 km / h braked sharply on an asphalt highway. The friction coefficient is 0.4.

A car moving at a speed of 60 km / h braked sharply on an asphalt highway. The friction coefficient is 0.4. Show that the braking time is independent of the vehicle weight.

Given:
v1 = 60km / h = 50/3 m / s,
v2 = 0,
μ = 0.4;
To find:
t -?
For uniformly accelerated motion, the speed is given by the formula:
v2 = v1 – a * t;
From here we find:
t = v1 / a;
According to Newton’s second law, the acceleration of a car is:
a = F / m;
where is the friction force
F = μ * P = μ * m * g;
Here
g = 10m / s ^ 2 – free fall acceleration;
We get:
a = μ * g;
t = v1 / (μ * g);
This shows that the braking time does not depend on the mass of the car:
t = 4.167s.