Question

This question is typical on some driver’s license exams: A car moving at 45 km/h skids 15 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

from kinematics equation if we know that final speed is ZERO and initial speed is given that due to constant deceleration the object will stop in some distance "d" and this distance can be calculated by kinematics

$v_f^2 - v_i^2 = 2 a d$

$0 - v^2 = 2(a)d$

here acceleration due to friction will be same at all different speed

so for 45 km/h speed the distance of stop is 15 m

while at other speed 112.5 km/h the distance will be unknown

now we will have

$0 - 45^2 = 2(a)15$

$0 - 112.5^2 = 2(a)d$

now divide above two equations

$\frac{45^2}{112.5^2} = \frac{15}{d}$

$d = 93.75 m$

So it will stop in distance 93.75 m