Here is a physics applet to help you visualize what a position vs. time graph looks like in motion.
(Make sure to click the gray "x vs. t" button next to "Constant Velocity" to see graphs relevant to this section)
You can see that the pink and red dots are moving in opposite directions at different speeds, while the blue dot is staying in place. The "x vs. t" or position vs. time graph shows this over 4 seconds.
Another fun simulation that you can play with to see how position and velocity relate is with the PhET moving man simulation
1. Click the green "Run Now" button and click on the "Graphs" tab at the top. Click on the red "minus" box at the top right of the acceleration graph - you won't be needing it for this activity. Make sure the "Record" button is clicked.