Answer to Question #98433 in Physics for Nyx

Question

This question is typical on some driver’s license exams: A car moving at 40 km/h skids
15 m with locked brakes.
How far will the car skid with locked brakes
at 100 km/h? Assume that energy loss is due
only to sliding friction.
Answer in units of m.
Don't round answer

Answer 1

Since the sliding friction in both cases is the same, so acceleration is same too.

The distance traveled by a car to the rest is given by

$$d=\frac{v_i^2}{2a}$$

So

$$\frac{d_2}{d_1}=\frac{v_{i2}^2}{v_{i1}^2}$$

$$\frac{d_2}{15\:\rm m}=\frac{100^2}{40^2}=6.25$$

Finally

$$d_2=6.25\times 15\:\rm m=93.75\: m$$