Position vs time graphs compared to velocity vs time graphs help?

Question

okay I have a velocity vs time graph and I got to draw the position vs time graph, and im not sure if im doing it right..the points for velocity are -2.75 at .5 secs -2.25 at 1.5 secs -1.75 at 2.5 secs -1.25 at 3.5 secs -.75 at 4.5 secs -.25 at 5.5 secs

Now I draw my position vs time graph, where do my points go?
I think its 0 at 0 secs -2.75 at 1 sec then -5 at 2 secs then 6.75 at 3 secs 8 at 4 secs 8.75 at 5 secs and 9 at 6 secs.

So this would make him slowing down in the negative direction. I get kind of confused with the negative direction thing, because the slope of the velocity is in the positive direction but its a negative velocity, what would happen if the line started in the negative velocity but crossing into positive velocity would the position then switch and he would be traveling in the postivie direction?

Answer 1

Yes, everything you said is correct (just make sure to keep up with the negative signs in your position function).

Currently, the velocity is negative, but moving toward becoming positive. That means the object in question is moving down (or left--whatever your negative direction is), at a slower and slower rate; when the velocity hits zero the object will stop moving. Then, when velocity becomes positive, the object will start to rise again, faster and faster.

Your object has a linear velocity (v=-3+t/2), so it has quadratic position (h=.25t^2 - 3t, assuming h=0 when t=0).