Someone please help me solve this physics problem! i have the answer..just don't know how to derive it!?

Question

question: a 2.1 x 10^3 kg car starts from rest at the top of a driveway that is sloped at an angle of 20.0 degrees with the horizontal. an average friction force of 4.0 x 10^3 N implodes the car's motion so that the car's speed at the bottom of the driveway is 3.8 m/s. What is the length of the driveway?

(question involves work-kinetic thm)

answer: 5.1m

how do you get this answer?

Answer 1

Start with determining the net force of gravity generated by the car
Fg=ma
a=g*Sin (20)
therefore
Fg=2.1 *10^3 kg* 9.8 m*sec^-2* Sin (20)
=7.0 N

Friction Force= 4.0*10^3 N
Net Force= Fg-FF=7.0-4.0=3.0*10^3 N

From here, I'll solve it two ways. The first is the way you are probably use to:

Now go back to F=ma to find the accleration downward
a=F/m
a=3.0*10^3 N /2.1 *10^3 kg
=1.43 m*sec^-2

Now
a=v/t
t=v/a
=3.8 m/sec / 1.43 m*sec^-2
=2.66 sec

Now
d=1/2 a t^2
=1/2 * 1.43 m*sec^-2 * (2.66sec)^2
=5.054 m
~5.1 m

Second way to solve it involves Work, Friction Energy etc.

Energy = F*d
KE at bottom= 1/2 mv^2
=1/2*2.1 x 10^3 kg* (3.8 m/s)^2
=15.2*10^3 J

Now, from above, net force =
F=3.0*10^3 N
E=F*d
d=E/F
d=15.2*10^3 J/3.0*10^3 N
=5.07m
~5.1 m