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Main content

Current time:0:00Total duration:3:57

AP.CALC:

CHA‑3 (EU)

, CHA‑3.B (LO)

, CHA‑3.B.1 (EK)

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 speeding up slowing down or neither so pause this video and see if you can figure that out alright now let's do it together and first we just make we need to make sure we're reading this carefully because they're not asking is the velocity increasing decreasing or neither they're saying is the object speeding up slowing down or neither so they're talking about speed which is the magnitude of velocity you can think of it as the absolute value of velocity especially when we're thinking about it in one dimension here so even though they're not asking about velocity I'm going to actually want to answer both so that we can see how sometimes they move together velocity and speed but sometimes they might one might be increasing while the other might be decreasing so if we look at this point right over here where our velocity is two meters per second the speed is the absolute value of velocity which would also be two meters per second and we can see that the slope of the velocity time graph is positive and so our velocity is increasing and the absolute value of our velocity which is speed is also increasing a moment later our velocity might be two point one meters per second and our speed would also be two point one meters per second that seems intuitive enough and we get the other scenario if we go to this point right over here our velocity is still positive but we see that our velocity time graph is now downward sloping so our velocity is decreasing because of that downward slope and the absolute value of our velocity is also decreasing right at that moment our speed is two meters per second and then a moment later it might be 1.9 meters per second alright now let's go to this point so this point is really interesting here we see that our velocity the slope of the tangent line is still negative so our velocity is still decreasing but what about the absolute value of our velocity which is speed well if you think about a moment before this we were slowing down to get to a zero velocity in a moment after this we're going to be speeding up to start having negative velocity you might say well it's beating up for negative velocity remember speed is the absolute value so if your velocity goes from zero to negative 1 m/s your speed just went from zero to one meter per second so we're slowing down here and we're speeding up here but right at this moment neither is happening we are neither speeding up nor slowing down now what about this point here are the slope of our velocity time graph or the slope of the tangent line is still negative so our velocity is still decreasing but what about speed well our velocities become is already negative and it's becoming more negative so the absolute value of velocity which is two meters per second that is increasing at that moment in time so our speed is actually increasing so you notice here you see a difference now what about this point well the slope of the tangent line here our velocity time graph is zero right at that point so that means that our velocity is not changing so you could say velocity not changing and if speed is the absolute value or the magnitude of velocity well that will also be not changing so we would say speed is I'll just say neither slowing down or nor speeding up last but not least this point right over here the slope of the tangent line is positive so our velocity is increasing what about speed well the speed here is two meters per second remember it'd be the absolute value of the velocity and he and the absolute value is actually going down if we forward in time a little bit so our speed is actually decreasing we are slowing down as our velocity gets closer and closer to zero because the absolute value is getting closer and closer to zero