Question

Each of the three plates has a mass of 10 kg. if the coefficients of static and kinetic friction at each surface of contact are μs = 0.3 and μk = 0.2 , respectively, determine the acceleration of each plate when the three horizontal forces are applied.

Answer 1

Even though you forgot to include the diagram of the problem, I found a similar problem as shown in the top of the picture. The diagrams at the bottom are force diagrams of each plate.

For plate D, the forces acting on it are the horizontal force 18 N, and the opposite frictional force which is equal to uk*W = 0.2(10 kg)(9.81 m/s²) = 19.62 N.
F = ma
19.62 N - 18 N = 10 kg(a)
a = 0.162 m/s²

For plate C, the forces acting on it are: horizontal 100 N, and the two opposite frictional forces from the top and bottom plates D and B.
F = ma
100 N - 2(19.62 N) = (10 kg)(a)
a = 6.076 m/s²

For plate B, because A is not moving, we use us instead of uk.
F = ma
0.3(10 kg)(9.81 m/s²) - 15 N = (10 kg)(a)
a = 2.943 m/s²