W = -Fd
W = [tex]\Delta[/tex]KE
W = (1/2)mv2^2 - (1/2)mv1^2
-Fd = -(1/2)mv1^2
but F = [tex]\mu[/tex]s(mg)
-[tex]\mu[/tex]s(mg)d = -(1/2)mv1^2
[tex]\mu[/tex]sgd = (1/2)v1^2
v1 = sqrt(2[tex]\mu[/tex]gd)
The flaw in your method was that you were using newton's second law, F = ma. While it's true in this case that the only force affecting the car's velocity is static friction, and so this is equal to ma, you don't know what a is, so it's necessary to formulate it differently.
It is against forum rules to provide complete solutions to homework questions. But anyway, you've make a mistake in your answer.
The rules can be found at: https://www.physicsforums.com/showthread.php?t=5374
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