How far will the car skid with locked brakes at 112.5 km/h? Assume that energy loss is due only to sliding friction. Answer in units of m.

Question

This question is typical on some driver’s license exams: A car moving at 45 km/h skids 12 m with locked brakes. How far will the car skid with locked brakes at 112.5 km/h? Assume that energy loss is due only to sliding friction. Answer in units of m.

Answer 1

Christina,

Assume the car while skidding moves with constant acceleration (actually, deceleration as it would be opposite to the velocity). That acceleration would depend only on the mass of the car and coefficient of kinetic friction between its tires and the road and therefore would not depend on the starting speed

Use a standard expression braking distance d, starting speed v₀ and acceleration a

1. v₀²=2ad so, d=v₀^2/2a (1)

We see from (1) that d is directly proportional to v₀² . Therefore comparing the 2 examples (when

(v₀)₁=45km/hr and (v₀)₂=113.5km/hr

we would get from (1)

d₂/d₁=[(v₀)₂]²/(v₀)₁]²=[(v₀)₂/(v₀)₁]²=(113.5/45)²=6.36 (2)

Therefore, d₂=(d₂/d₁)d₁=6.36x12m=76m (3)

(we left only 2 significant figures as that of the least accurate data given (,45km/hr and 12m)

Hope that is helpful,

Dr.Ariel B