Question

A detective is investigating a scene of an accident. He measures the length of an automobile's skid marks to find out how fast the automobile was going at the very beginning of the skid. Express In terms of V ( speed), L ( length) and any other suitable variables related to this problem

Answer 1

initial speed = V
final speed = 0

length of skid = L
assume constant road/tire friction coefficient = mu
a = magnitude of deacceleration
0 = V - a t
so
t = V/a time to stop
L = V t - (1/2) a t^2
L = V(V/a) - (1/2)a(V^2/a^2)
so
L = (1/2)(V^2/a)
a = V^2/2L
now physics
F = m a = mu m g
mu m g = m V^2/L
L mu g = V^2
so
V = sqrt(mu g) sqrt L
g = 9.81 m/s^2
I bet the detective knows mu for tire and road
So he can estimate speed V from skid length L
breaking force = F = -

Answer 2

why is it
mu m g =m V^2/L instead of mu m g= m V^2/2L?

Answer 3

sorry, missed the 2

Answer 4

I checked the units but not the constants