How do I figure out the initial velocity of an object?

[Dobro_player]

Homework Statement

Hi, I need to figure out the initial velocity if an object of 1400 kilograms is subjected to a friction coefficient (sliding friction) of 0.4587 for 75.6 metres, and its final velocity after being subjected to that friction is 23.05 metres per second. How do I go about this?

Homework Equations

The only equations that I can think of that are relevant is:
Fr=μmg
distance=ut+0.5at²
Ek=0.5mv

The Attempt at a Solution

Friction force= Fr=μmg
Fr=0.4587*1400*9.8=6293.364
Final momentum
p=mv
p=32270N
Final Kinetic energy
Ek=0.5mv
Ek=0.5*1400*23.05=16135J
I'm not sure how to do the distance equation as I don't know the amount of time.

 

[Doc Al]

Two ways to go:
(1) Use kinematics. Use Newton's 2nd law to find the acceleration and combine that with some kinematic equations. (Look for a kinematic relationship that includes distance and velocity.)
(2) Use energy. What's the work done by that friction force?

FYI: KE = ½mv², not ½mv.