This is the question:
A rope brings a 50 kg object downward at an acceleration of 0.75. What is the tension force of the rope?
I thought that, since the tension and the weight are both "going" downward, the net force would be Weight + Tension = Mass x -Acceleration. The acceleration is negative because it is going downward. But if I do it that way I get the wrong answer. The answer is only correct if net force is Weight - Tension, and if acceleration is positive, neither of which makes sense to me. Can someone explain this?
It could be a silly arithmetic error that I haven't noticed.
Answer
Because the tension points upwards. Notice that the acceleration you gave is less than $g$, and thus $T$ opposes gravity. Choosing the positive axis up, the correct equation is
$$T-mg=ma$$
with $a<0$ as you stated.
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