Use Work (net) to find coefiicient of static friction and speed

1. a 5.0 kg block is pushed up a wall by a 90N force. Assume that the block starts from rest and that it has an acceleration of 0.5m/s^2.

a. find the coefficient of kinetic friction between the block and the wall.
b. Find the work done by each force acting on the block.
c. Find the speed of the block after it has moved 3.0m up the wall.

I broke the 90N force into x and y components, but it made it difficult to see what work done by other forces was negative or zero, so I then made the 90N force point in the positive x direction, so that Ncos(55) = zero, Nsin(55) = m*g*sin(55) = 40.1N, and the work done by friction and weight equal zero in the -x (cos(55)) direction. and work done by weight = -m*g*sin(55) = -40.1, but other than knowing the work done by friction is = -μk*N*sin(55), I don’t know how to solve for μk.

Also I think it’s weird that work done by the normal force cancels out work done by the weight force – they are in opposite directions so it makes sense, but I thought I should be able to add up all the forces involved and get zero – is that not true because there is acceleration?

Should I be using the acceleration given in the problem instead of the acceleration due to gravity?

I think that the total work is equal to work of friction, plus normal, plus weight, plus the 90N force (some of these are negative of course), and that that number is = 0.5*m*v^2, and that will be how I solve for c. Basically I’m really stuck on a. – finding the coefficient of kinetic friction. Once I have that, I can calculate the work done by friction and complete part b., and use that part to solve for c – only I don’t know how to plug in the 3.0m – I know it will have something to do with the acceleration given but I’m not sure what.

So to sum up my questions – how do I find the coefficient of kinetic friction?
What does the acceleration being equal to 0.5 mean for how I solve/think about this problem, and does it replace g?
How am I supposed to use the information in part c (distance traveled) to solve for the velocity at that point?

And of course, are my thoughts above laid out correctly or am I trying to use the wrong expressions to solve this problem?

Thank you.

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