# Question for Physics?

This question is typical on some driver’s li- cense exams: A car moving at 42 km/h skids 12 m with locked brakes.

How far will the car skid with locked brakes at 84 km/h? Assume that energy loss is due only to sliding friction.

Relevance
• d' = d*(V'/V)^2 = 12*2^2 = 48 m

• To solve this problem, you need the car’s acceleration. Use the following equation.

vf^2 = vi^2 + 2 * a * d, vf = 0

0 = vi^2 + 2 * a * d

vi^2 = -2 * a * d

a is constant.

As I look at this equation, I can see that the distance is inversely proportional to the square of the velocity. Since the new velocity is twice the original velocity. To me, this means the new distance will be four times the original distance. The first step is to convert the velocities from km/h to m/s.

1 km = 1,000 m

1 h = 3,600 s

1 km/h = 1,000/3,600 = 5/18 m/s

v1= 42 * 5/18 = 11⅔ m/s

v2 = 84 * 5/18 = 23⅓

0 = 11⅔^2 + 2 * a * 12

a = -11⅔^2 ÷ 24

The car’s acceleration is approximately -5.67 m/s^2. Let’s use this number and the new velocity in the same equation.

0 = 23⅓^2 + (2 * -11⅔^2 ÷ 24) * d

d = 23⅓^2 ÷ (11⅔^2 ÷ 12) = 4 * 12 = 48 meters

This is exactly four times the original distance. I hope this is helpful for you.

• this requires knowledge of the laws of motion, and would not be on any driver license exam.