Question

Solve for final velocity (vf) from this equation: kf = FD + (1/2)M((vi)^2). (This stems from the formula for work.)

Answer 1

Can you clarify your variables?

Answer 2

F = force
D = distance
M = mass

Answer 3

kf?

Answer 4

Well, W = Kf - Ki. Kinetic friction or something?

Answer 5

I am going to make a recommendation try looking at it in a different way.
Work = The change in Energy but it is also equal to the forces times the total displacement that the object undergoes. \[w=\Delta E=\frac{1}{2}m(v_{2}^2-v_{1}^2)\]

but you know also that \[w=fdcos\theta\] if the force is constant otherwise you have to deal with intergrals. so set the two equal to one another and find v_{2}