Question

A car travels with velocity v₀ = 100 km/h. At time t = 0, the driver fully applies the brakes. At that moment the car starts sliding on a rough road (coefficient of kinetic friction µ). Use the simplest model for the car (point mass) and calculate the time t^∗ and the distance t^∗ until the car comes to a stop a) on a dry road (µ = 0.8), b) on a wet road (µ = 0.35).

Answer 1

The equation of motion in the horizontal direction 

← : ma = mx¨ = −R ,

the equilibrium condition in the vertical direction 

↑ : 0 = N − mg

and the law of friction R = µN 

lead to

a = −µg .

Integration with v(t= 0) = v₀ and x(t= 0) = 0 yields

v(t) = v₀ − µgt ,

The time t ∗ follows from the condition v = 0:

t ∗ = v₀/µg

This leads to

a) On a dry road (µ = 0.8) we obtain

b) On a wet road (µ = 0.35) we are led to