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# Interpreting direction of motion from position-time graph

AP.CALC:
CHA‑3 (EU)
,
CHA‑3.B (LO)
,
CHA‑3.B.1 (EK)

## Video transcript

an object is moving along a line the following graph gives the object's position relative to its starting point over time for each point on the graph is the object moving forward backward or neither so pause this video and try to figure that out alright so we see we have position in meters versus time so for example this point right over here tells us that after one second we are four meters ahead of our starting point or for example this point right over here says that after four seconds we are almost it seems almost four meters behind our starting point so let's look at each of these points and think about whether we're moving forward backward or neither so at this point right over here at that moment we're about two and a half meters in front of our starting point we're at a positive position of two and a half meters but as time goes on we are moving backwards closer and closer to the starting point so this is we are moving backward one way to think about it at this time we're two and a half meters if you go forward about half a second we are then back at our starting point so we have to go backwards and if we look at this point right over here it looks like we were going backwards this entire time while our curve is downward-sloping but at this point right over here when we are about it looks like five meters behind our starting point we start going forward again but right at that moment we are going neither forward nor backwards it's right at that moment where we just finished going backwards and we're about to go forward and one way to think about it is what would be the slope of the tangent line at that point and the slope of the tangent line at that point would be horizontal and so this is neither so we can use that same technique to think about this point the slope is positive and we see that all right right at that moment it looks like we are at the starting point but if you fast for even a few even a fraction of a second we are now in front of our starting point so we are moving forward we are moving forward right over here and at this point we are at our starting point but if think about what's going to happen a moment later a moment later we're going to be a little bit behind our starting point and so here we are moving backward and we're done