Answer
The car was traveling at a speed of 25.2 m/s.
Work Step by Step
We can find the magnitude of the car's deceleration.
$F_f = ma$
$mg~\mu_k = ma$
$a = g~\mu_k$
$a = (9.80~m/s^2)(0.50)$
$a = 4.90~m/s^2$
We can use the rate of deceleration to find the initial velocity of the car.
$v_f^2 = v_0^2+2ax$
$v_0^2 = 0-2ax$
$v_0 = \sqrt{-(2)(-4.90~m/s^2)(65~m)}$
$v_0 = 25.2~m/s$
The car was traveling at a speed of 25.2 m/s
