Finding the speed of a car?

Question

A 1500kg car skids to a halt on a wet road where u sub k= 0.55.

1.) How fast was the car traveling if it leaves 67m--long skid marks?

Answer 1

Did it start from rest?

0.55={F-[1500kg*((Vf^2-Vi^2)/2(67m)]} divided by (1500kg*9.8m/s/s)

Answer 2

Coefficient of friction uk = 0.55

Mass m = 1500 kg

Assuming horizontal road,

normal force on the car by the road = weight of the car = 1500 * 9.8 N = 14700 N

Force of friction on the car f = uk * normal force = 0.55 * 14700 N = 8085 N

Acceleration a = -f/m = -8085/1500 = -5.39 m/s^2

(negative because friction is opposite to motion)

Displacement s = 67 m

Final velocity v = 0

Initial velocity u = ?

v^2 = u^2 + 2as

Or, 0 = u^2 - 2 * 5.39 * 67

Or, u^2 = 2*5.39*67

Or, u^2 = 722.26

Or, u = sqrt(722.26) = 26.87 m/s

Ans: 26.87 m/s