Ahorizontal force of 30 n pulls a block of mass 2.5 kg across a level floor. the coefficient of kinetic friction between the block and the floor is μk = 0.25. if the block begins with a speed of 7.0 m/s and is pulled for a distance of 14 m, what is the final speed of the block?

We want to find vf. We're given vi and d. An equation that incorporates all these variables is:

vf^2 = vi^2 + 2ad

You'll notice we're missing an acceleration, a. However, we can figure this out using the rest of the information given in the question. We know the acceleration is going to be related to the net force, F(net), give by F(net) = ma. The net force is going to be the combination of the applied force and the frictional force; in other words:

F(net) = F(app) - f
ma = F(app) - umg
2.5a = 30 - 0.25(2.5)(9.8)
a = 9.6 m/s^2

Now we can plug this value into the original equation:

vf^2 = vi^2 + 2ad
vf^2 = 7^2 + 2(9.6)(14)
vf = 17.8 m/s