Answer
The initial speed of the car was 34 m/s.
Work Step by Step
The force of kinetic friction acted against the car's motion to bring the car to a stop. Let's calculate the magnitude of the acceleration caused by the force of kinetic friction.
$ma = F_f$
$ma = mg~\mu_k$
$a = g ~\mu_k$
$a = (9.8 ~m/s^2)(0.80)$
$a = 7.8 ~m/s^2$
The magnitude of acceleration is $7.8 ~m/s^2$. Because the car was decelerating, the acceleration is $-7.8 ~m/s^2$.
$v^2 - v_0^2 = 2ax$
$0 - v_0^2 = 2(-7.8 ~m/s^2)(72 ~m)$
$v_0 = \sqrt{(2)(7.8 ~m/s^2)(72 ~m)}$
$v_0 = 34 ~m/s$
The initial speed of the car was therefore 34 m/s.
