A cord is used to lower an initially stationary block at a constant downward acceleration for distance d?

Question

A cord is used to vertically lower an initially stationary block of mass M kg at a constant downward acceleration of g/4. The block has fallen a distance d.

(a) Find the work done by the cord's force on the block. (Answer in terms of M, g, and d.)

(b) Find the work done by the weight of the block.

(c) Find the kinetic energy of the block.

(d) Find the speed of the block. (Assume the positive direction is downward.)

Answer 1

Using F=M*a, consider a FBD of the block
M*a=-M*g/4=T-M*g
The tension in the cord is T
T=M*g-M*g/4
T=3*M*g/4

The work done by T is
-3*M*g*d/4

The work done by the Weight of the block is M*g*d
the net is equal to the kinetic energy, or
M*g*d/4

This is related to the speed of the block, v, as
.5*M*v^2=M*g*d/4
v=sqrt(g*d/2)

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Answer 2

inT=3*Mg/4 -
where did the 3 come from?