Question regarding Negative Velocity

[Drewski]

On a Position-Time Graph, if you start with a negative velocity and slowly increase (Accelerate) in velocity, would you have a negative position that increases to a positive position?

In other words, would it look like this?

Velocity-Time Graph on the Right, Position Time-Graph on the Left. Are they correct?

 

[mikeph]

If your acceleration is in the positive direction, then your v/t graph is correct but your x/t graph is wrong: it should look like a parabola, not two straight lines.

 

[jtbell]

would you have a negative position that increases to a positive position?

It depends on the initial position. If the initial position is zero, then you have something like your graph (I assume you meant to draw a smooth parabola but were limited by your tools ). If the initial position is positive and "large" enough, the graph stays above the horizontal axis and the position never becomes negative.