Question

A car skids 18 m on a level road while trying to stop before hitting a stopped car in front of it. The two cars barely touch. The coefficient of kinetic friction between the first car and the road is 0.80. A policewoman gives the driver a ticket for exceeding the 35 mi/h speed limit.
Determine the initial speed of the car.

Answer 1

Answer:

16.80856 m/s or 37.6 mph

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity = 0

s = Displacement = 18 m

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s²

$a=-\frac{f}{m}\\\Rightarrow a=-\frac{\mu mg}{m}\\\Rightarrow a=-\mu g$

$v^2-u^2=2as\\\Rightarrow v^2-u^2=2(-\mu g)s\\\Rightarrow -u^2=2(-\mu g)s-v^2\\\Rightarrow u=\sqrt{v^2-2(-\mu g)s}\\\Rightarrow u=\sqrt{0^2-2\times (-9.81\times 0.8)\times 18}\\\Rightarrow u=16.80856\ m/s$

The initial speed of the car is 16.80856 m/s

Converting to mph

$1\ m/s=\frac{1}{1609.34}\times 3600\ mph$

$16.80856\ m/s=16.80856\times \frac{1}{1609.34}\times 3600\ mph=37.6\ mph$

The initial speed of the car is 37.6 mph