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## Homework Statement

First, let us consider a sled of mass m being pulled by a constant, horizontal force of magnitude F along a rough, horizontal surface. The sled is speeding up.

Let us now consider the situation quantitatively. Let the mass of the sled be m and the magnitude of the net force acting on the sled be F. The sled starts from rest.

Consider an interval of time during which the sled covers a distance s and the speed of the sled increases from v

_{1}to v

_{2}. We will use this information to find the relationship between the work done by the net force (otherwise known as the net work) and the change in the kinetic energy of the sled

Use W=Fscos(θ) to find the net work W

_{net}done on the sled. Express your answer in terms of some or all of the variables m, v

_{1}and v

_{2}.

## Homework Equations

W=Fscos(θ)

K=1/2mv

^{2}

ƩF=ma

## The Attempt at a Solution

The only thing I could do so far is the equation for F

_{net}. The equation is unsimplified, so it is a little messy, but I attatched a picture of the F

_{net}equation.

Since W

_{net}=F

_{net}s, I assumed that if you multiply by s, the distance, then the s would cancel out and you would be left with the net force equation without the s in there. However, I'm very confused by what it is asking. It says that W=Fscos(θ), but the answer cannot have the variable θ in there. The only thing I could think of is that since it is being pulled on a flat surface, then cos(180°)=-1, but since the sled is speeding up in the direction of the net force, work has to be positive. I cannot figure out what I should do next to try to solve this.

Thank you in advance for the help.