Calculating tension in a winch cable

Question

I have the question:

Here is my attempt is this correct ?

(I would put this question on physics SE however every question I have put up so far is apparently "not related to physics" and is a "homework question")

Answer 1

Key concepts:

• Newton's first law
• Newton's second law
• If $a$ is uniform (/constant), then $a = \dfrac{v_f-v_i}{t}$

At rest: $$\sum F = T - mg = 0 \\ T = mg$$

Going up: $$\sum F = T - mg = ma \\ T = m(a+g) = m\left(\frac{v_f-v_i}{t}+g\right)$$

Going down: $$\sum F = mg - T = ma \\ T = m(g-a) = m\left(g-\frac{v_f-v_i}{t}\right)$$