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Wednesday, August 22, 2012

Motion Graphs and the Meaning of Slope on These Graphs

Here we take a look at a more visual way of analyzing motion, motion graphs.  These refer to those graphs of position vs time, velocity vs time, and acceleration vs time.  What is cool about these is that when you get good at reading the graphs, you can picture the motion of the object the graphs are describing.  We will use one of the ActivPhysics simulations (1.2) to help connect the initial conditions, the actual motion of a car, and the motion graphs to each other.  I recommend playing with these simulations on your own (1.2, 1.3), and you will find yourself getting better and better of making all the connections.

Now, for us we will include the calculus.  Specifically, slopes of the motion graphs are important.  And we now know that derivatives are really just slopes of graphs, even if they are curves.  This is what we are after in this video lesson.

velocity = slope of position graphs = dx/dt
acceleration = slope of velocity graph = dv/dt

Focus on these definitions as you watch.

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