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Now, the thing that I don't quite understand is,how would such a graph look like if the object were to move in two or three dimensions? Assuming it now moves in space, it could still be moving along a straight line, but what if it started moving in some other direction, how do the new velocities look like on a position vs. time graph? There seems to be a gap in my understanding at this point and I can't quite connect how the slope of a position vs. time graph would represent the change in velocity.

I hope I stated my concerns clearly and I'm looking forward to any sharing of thoughts on this matter.

Thanks