For this problem, we will be looking at the work energy theorem and how it applies to several different forces in the system. The first force we will be looking at is this pushing force that is applying 130 Newton's on the box, which is causing it to slide along the floor. The work done by this force is equal to the magnitude of the force times the distance that the box travels, which is 130 Newton's times the five metres, which gives 650 jewels. Notice that the work done by this force is positive because the force and the displacement of the box are pointing in the same direction. The second force will be looking at is the fresh and force. This the work done by this force is going to be the negative of the friction force times the distance at the box travels. In this case, because the friction forces opposing the motion of the box, the work done by this force is negative. The first enforce can be found by using by multiplying the coefficient refreshing times normal force and the normal forces simply just the weight of the box. It's mass times gravity, which is 40 kg times 9 21 meters per second squared, which gives a normal force of 392 0.4 newton's to find the first enforce, we multiply the 392 0.4 Nunes by the coefficient of friction, which is 0.3 which gave 117 Yeah 0.72 newtons. Now we can plug back into the work formula which gives us that the work done by the friction forces negative 117.72 newtons times of five m of the box travels, which gives us negative 588 0.6 jewels. Now we can look at the work done by the normal force. This is simple because the law enforces pointing straight up while the box is only being displaced in the horizontal direction, which means that the work done by this force zero. Similarly, the work done by gravity is also zero because the force of gravity is pointing straight down and the blocks only moves left and right. Now we can think about the kinetic change in kinetic energy that the force experience during this movement. The change in kinetic energy, it's equal to the work non conservative done by all the forces in the system. In this case, both the pushing force of 130 Newton's and the frictional force are non conservative, which means that the change in kinetic energy is equal to the work done by the pushing force minus the work plus the work done by the frictional force, which gives us that. The change in kinetic energy is 650 jewels minus the 588 0.6 jules, which means that the change in kinetic injury is 61 point or jewels notice that it I subtracted 588.6 jewels because we found that that work done by the frictional force was negative since it opposed the motion. Finally, we can find the final velocity of the box. Since we know the change in kinetic energy is equal to 61.4. This must be equal to one half the math. The box times the final velocity squared minus one half the the mass of the blocks, times the initial velocity squared. We know that the initial velocity of the boxes zero since it started at rest, which can souls this term to zero. So we're left with 61.4 is equal to one half the mass of the box, which is 40 kg times the final velocity squared. This allows us to find the final velocity, which is 1.75 meters per second.