Answer
The speed of car A when it started sliding was $~~4.6~m/s$
Work Step by Step
We can find the magnitude of deceleration as the car slides:
$F = ma$
$mg~\mu_k = ma$
$a = g~\mu_k$
$a = (9.8~m/s^2)(0.13)$
$a = 1.27~m/s^2$
We can find the velocity $v_0$ of car A when it started sliding:
$v_f^2 = v_0^2+2ax$
$0 = v_0^2+2ax$
$v_0^2 = -2ax$
$v_0 = \sqrt{-2ax}$
$v_0 = \sqrt{-(2)(-1.27~m/s^2)(8.2~m)}$
$v_0 = 4.6~m/s$
The speed of car A when it started sliding was $~~4.6~m/s$
