Please help , physics question

Question

A car moving at 49 km/h skids 12m with locked breaks. How far will the car skid with locked brakes at 122.5 km/h ? Assume that energy loss is due only to sliding friction. Answer in units of m.

Answer 1

Let's use SI units. 49 km/h x 1000m/3600s = 13.611 m/s and 122.5 km/hr = 34.028 m/s

The initial energy (kinetic) = 1/2mv² = 1/2m(110/9)² = 92.631m joules

The final energy = 0

Then the work done is 92.631m joules (lost due to friction)

F_F = μN = μmg = 9.81μm

Work = Fd = (9.81μm)(12) = 117.72μm

So 117.72μm = 92.631m or 117.72μ = 92.631 meaning μ = 92.631/117.71 = 0.7869

If the car is traveling 34.028 m/s (122.5 km/hr) then its kinetic energy = 1/2mv² = 1/2m(34.028)² = 578.94m joules

The work will be Fd = μNd = μmgd = (0.7869)m(9.81)d = 7.7193md

So 578.94m = 7.7193md or 578.94 = 7.7193d meaning d = 578.94/7.7193 = 75 m