Please help me understand this velocity time graph

[UnD3R0aTh]

can u describe this motion? how is x > 0 at E? how can we tell the sign of x from the graph?

 

[DrClaude]

This looks like a harmonic oscillator centered on $x=0$. In that case, $a=0$ corresponds to $x=0$ and the acceleration is pointing to the left ($a <0$) when the particle is right of $x=0$. Therefore $a < 0$ means $x > 0$, which is the case for $t_\mathrm{E}$.

 

[Simon Bridge]

can u describe this motion?

"u" wouldn't, but "you" would describe it by looking at the shape - what shape is it? What class of equations gives that shape?

how is x > 0 at E? how can we tell the sign of x from the graph?

x is the displacement - what is the relationship between the displacement and the velocity?
You cannot actually tell the absolute position of the object just from looking at the v-t graph alone - you can only tell how it changes position.