\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)
Chapter 3: Linear Motion
13.

Graphing Position

Another we can visualize motion, particularly in one dimension, is by graphing the position, velocity, or acceleration as a function of time. Time is always on the horizontal axis in such graphs.

To make a position graph we need to define an origin (the point which we are calling "0") and a direction we're calling "positive" (often to the right, by convention.) The axis is usually labelled $x$ if the motion is horizontal and $y$ if it is vertical, although that's also a matter of convention: for an object moving along a diagonal, for instance, we could use either label.

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The motion diagram of an object that moves to the left at a constant speed. The origin is chosen in the middle of this line.
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The corresponding graph for this object. The dots are not essential to the graph, but are useful for constructing the graph from the motion diagram: for each dot on the motion diagram, place a dot at the same value of $x$ and $t$. Constant velocity corresponds to a linear position graph.
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The motion diagram of a block oscillating on a spring: it moves to the left, stops, and goes back to the right. (I've shifted some of the dots down so they don't overlap.)
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This is the corresponding graph. The minimum or maximum of a position graph is called a turning point, and occurs when the object changes direction.