Question is too long, so it's in the explanation box.. Please help!
During the investigation of a traffic accident, police find skid marks 135.1 m long. They determine the coefficient of friction between the car's tires and the roadway to be 0.607 for the prevailing conditions. Estimate the speed of the car when the brakes were applied in m/s.
Let us say at the braking the vehicle speed was V.
At the moment that brake is applied the vehicle has a kinetic energy.This energy will be used for friction when it brakes and due to friction the vehicle stops.The braking distance is given by the skid length.
By law of conservation of energy we can say;
kinetic energy = work done against friction
`1/2*m*v^2 = mu*R*d`
`1/2*m*v^2 = mu*mg*d`
`1/2*v^2 = mu*g*d`
`v^2 = 2mugd`
`v = sqrt(2mugd)`
`v = sqrt(2*0.607*9.81*135.1)`
`v = 40.11m/s`
So the speed of the vehicle had been 40.11m/s.
In terms of km/h the speed is 144.4 km/h.
- All the kinetic energy had been used against the friction at the braking