Seemingly simple mechanics questions

[werproc]

1. Homework Statement
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)?

Homework Equations

:
F=ma, mg etc.[/B]

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

 

[haruspex]

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

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.

 

[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

 

[haruspex]

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

Note the constraint mentioned here:

weight mg and a string that is less of magnitude with tension t