Interpreting direction of motion from velocity-time graph | AP Calculus AB | Khan Academy

An object is moving along a line. The following graph gives the object's velocity over time. For each point on the graph, is the object moving forward, backward, or neither? So pause this video and see if you can figure that out.

All right, now let's do this together. We can see these different points on this velocity versus time graph. The important thing to realize is that if the velocity is positive, we're moving forward. If the velocity is negative, we're moving backward. If the velocity is zero, we're not moving either forward nor backward, or neither forward nor backward.

So right over here, we see that our velocity is positive—it's a positive two meters per second. So that means that we are moving forward. Now, over here, our velocity is zero meters per second, so this is neither. Now, over here, our velocity is negative four meters per second. One way to think about it is we're moving four meters per second backward, so I'll write backward.

Now, this is interesting, this last point, because you might be tempted to say, "All right, I'm oscillating. I'm going up, then I'm going down, then I'm going back up; maybe I'm moving forward here." But remember what we're thinking about here: this isn't position versus time; this is velocity versus time. So if our velocity is negative, we're moving backward.

And here, our velocity is still negative—it's becoming less negative, but it's still negative. So we are still moving; we are still moving backward. If we were at this point right over here or at this point, then we would be moving forward if our velocity were positive.