car's speed?

Question

at an accident scene on a level road ,investigator measure a car's skid mark to be 88mlong .the accident occured in arainy day the coeffecient of static friction 0.42etermine the speed of the car when the driver slammed on the brakesans why does the cr's mass doesnt matter

Answer 1

Kinetic energy Ke has to be converted into work Wf by friction to bring the suspects car to rest over distance S
Ke=Wf
0.5mV^2=umgS

V= sqrt(2u m g S/ m) masses cancel
V= sqrt(2 u g S)
V=sqrt( 2 x 0.42 x 9.81 x 88)
V=27 m/s or 97 km/h

PS
Coefficient of static friction is not much of use in the case of a skid marks we actually need a dynamic coefficient. And if you check in the table (see ref) it is a dynamic coefficient.

Answer 2

I think it's not the coefficient of static friction but the coefficient of kinetic friction.
Let m = mass of the car
Vi = initial speed of the car
Vf = final speed of the car = 0
μk = 0.42
dx = 88 m, length of the car's skid mark = distance traveled by the car from the moment the brakes were slammed to the moment the car stopped.

Find: Vi
Fa - Ff = ma
0 - μkFn = ma
- μk(mg) = ma
- μkg = a
a = - 0.42(9.8 m/s^2)
a = - 4.1 m/s^2

2adx = Vf^2 - Vi^2
2adx = 0^2 - Vi^2
2(-4.1 m/s^2)(88m) = - Vi^2
2(4.1 m/s^2)(88 m) = Vi^2
Vi = sqrt[2(4.1 m/s^2)(88 m)]
Vi = 26.9 m/s ANS

teddy boy

Answer 3

Read the book by Cooper on Motor Law. Every prosecutor and attorney has one