Determine when the velocity of the particle is zero

[you_of_eh]

A particle has an initial position X=0m and an initial velocity v=-6.0m/s. Its acceleration is given by the function [1.0 m/s^2 + (0.25 m/s^3)t] where t is in seconds.

Plot the acceleration vs. time. From your plot, determine when the velocity of the particle is zero.

-ok so if when I plot this line, because acceleration is always positive, wouldn't the line just have a constant positive slope. I know you're supposed to find the area under the curve to get the velocity. But when the velocity equals 0? I don't get how I could find this from my
a vs t graph.

 

[ideasrule]

-ok so if when I plot this line, because acceleration is always positive, wouldn't the line just have a constant positive slope.

Yes.

I know you're supposed to find the area under the curve to get the velocity.

Actually, the area under the curve is the change in velocity, not the velocity itself; that's why the question gives you the initial velocity. So if you want v=0, delta v has to be 6 since -6+6=0. When is the area under the graph 6?