Estimate the speed of the car when the brakes were applied?

Question

During the investigation of a traffic accident, police find skid marks 90.0 m long. They determine the coefficient of friction between the car's tires and the roadway to be 0.500 for the prevailing conditions. Estimate the speed of the car when the brakes were applied

What formula would I use here

Answer 1

a = µ*g = 4.9 m/s²

V = √(2ax) = √(2*4.9*90) = 29.7 m/s

Answer 2

Nice problem - it brings together two concepts.

First, the car is deccelerating over the 90 m and the force causing that decceleration is friction.  The force of friction is equal to the wieght of the car times the coefficient of friction, so you can write (using Netwon's laws)

ma = - umg  where u = coefficient of friction, m = mass of car and g = acceleration due to gravity (9.8 m/s^2).  Then the car experiences an acceleration of:

a = -ug  the minus sign indicats it is slowing down.

Now from kinematics, you know speed, distance and acceleration are related by:

x = (v^2 -v0^2)/(2a)  where v = final speed, v0 = initial speed

Since the car stops, set v = 0 and set x = 90m and a = -ug

x = -v0^2/(-2ug) = v0^2/(2ug)  solve for v0

v0 = sqrt(2ugx) = sqrt(2*0.5*9.8*90) = 29.7 m/s

Answer 3

The coefficient of kinetic friction μ is defined as the ratio of the friction force F  to the normal force N:

μ = F/N ---> F = μN

The normal force, which is equal to the weigh W = mg of the car does not affect the motion, only the friction force F = -μmg does. Once knowing the acting force, you can evaluate the acceleration/ deceleration, write the equation to calculate the change of velocity as a function of distance (v^2 - u^2 = 2as)