Seemingly simple mechanics questions

1. Mar 11, 2016

werproc

1. The problem statement, all variables and given/known data
The problem basically states that there is a box with weight mg and a string that is less of magnitude with tension t as shown in this picture: https://gyazo.com/efeb48469cfb44399bea6c2dcc9e87c7
The question is what are two possibilities for this situation and the answers are : rising with a decreasing speed and falling with an increasing speed. I do not understand the rising with a decreasing speed aspect of it in conceptual and mathematical terms. How does this happen (in what scenario for example)?

2. Relevant equations:
F=ma, mg etc.

3. The attempt at a solution
It's obvious that acceleration is negative from the start as mg has the greater magnitude (T-mg/m = a)
my thought was we either have an initial tension that decreases of some sort or we have an initial velocity above 0 for the box and it decreases as time goes on

2. Mar 11, 2016

haruspex

Do not assume the system was previously at rest, with only mg and T<mg acting on it since. The object may have been given an initial speed by some some larger T, or by some other means.

3. Mar 13, 2016

Kaura

That problems seems somewhat unspecific

I can think of scenarios in which at least the last two answers apply and possible the first two as well

I am curious as to what the answer is and why

4. Mar 13, 2016

haruspex

Note the constraint mentioned here:

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