It is accelerating: the distance moved is $d=vt+\frac{1}{2}at^2$ where $d$ is on the $x$ axis and acceleration from $F=ma$ where $F$ is on y-axis. It starts from rest so $v(0)=0$. The area under the curve is the work with respect to x-axis.
Move one unit right and you have case $\sum F_x=1$ and by Newtow's law, $F=ma$ so $a=\frac{F}{m}$ where $F=\sum F_x=1$ and $m\not =0$ so $a\not = 0$ so acceleration.
No, the box will stop at some spot -- it is impossible to tell. We cannot see when it stops.
It could start moving backwards with negative force.
But now this was the last one: I need to read for my exam. Post your question to the main site as simple as possible -- people will surely try to help.
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I had one from 11-12 (slot is till 12:30, but the teacher says that the course only needs 1hr per slot). Then I have chem lab from 2-5, but it'll get over in 15mins since its the first day
@CrazyBuddy note that a meta post may not always be a good idea. If you write a calm, well-written email to community@, you probably will get a better response. A meta post may cause unnecessary drama and may be taken the wrong way
Note that if a mod "retaliates" to something like this, that generally is cause for temporary removal of the diamond