Answer
The driver was moving at a speed of 65.6 mi/h when the driver started braking. Since the speed limit is 45 mi/h, the driver was guilty of speeding.
Work Step by Step
We can find the rate of deceleration.
$F_f = ma$
$mg~\mu_k = ma$
$a = g~\mu_k = (9.80~m/s^2)(0.750)$
$a = 7.35~m/s^2 = 24.11~ft/s^2$
We can use the acceleration to find the speed when the driver applied the brakes.
$v_0^2 = v^2-2ax = 0 - 2ax$
$v_0 =\sqrt{-2ax} = \sqrt{-(2)(-24.11~ft/s^2)(192~ft)}$
$v_0 = 96.2~ft/s$
We can convert the speed to units of mi/h.
$v_0 = (96.2~ft/s)(\frac{3600~s}{1~h})(\frac{1~mi}{5280~ft})$
$v_0 = 65.6~mi/h$
The driver was moving at a speed of 65.6 mi/h when the driver started braking. Since the speed limit is 45 mi/h, the driver was guilty of speeding.
