Okay, we are asked to draw three graphs, each of which has the time, the same “stopwatch
readings” plotted along the horizontal1 axis. The first thing I do is to ask myself whether the
plotted lines/curves are going to extend both above and below the time axis. This helps to
determine how long to draw the axes. Reading the description of motion in the case at hand, it is
evident that:
(1) The car goes forward of the start line but it never goes behind the start line. So, the
x vs. t graph will extend above the time axis (positive values of x) but not below it
(negative values of x).
(2) The car does take on positive values of velocity, but it never backs up, that is, it never
takes on negative values of velocity. So, the v vs. t graph will extend above the time
axis but not below it.
(3) The car speeds up while it is moving forward (positive acceleration), and it slows down
while it is moving forward (negative acceleration). So, the a vs. t graph will extend both
above and below the time axis.
Next, I draw the axes, first for x vs. t, then directly below that set of axes, the axes for v vs. t,
and finally, directly below that, the axes for a vs. t. Then I label the axes, both with the symbol
used to represent the physical quantity being plotted along the axis and, in brackets, the units for
that quantity.
Now I need to put some tick marks on the time axis. To do so, I have to go back to the question
to find the relevant time intervals. I’ve already read the question twice and I’m getting tired of
reading it over and over again. This time I’ll take some notes:
At t = 0: x = 225 m
v = 15 m/s
0-5 s: v = 15 m/s (constant)
5-10 s: v increases steadily from 15 m/s to 35 m/s
10-20 s: v decreases steadily from 35 m/s to 0 m/s
From my notes it is evident that the times run from 0 to 20 seconds and that labeling every
5 seconds would be convenient. So I put four tick marks on the time axis of x vs. t. I label the
origin 0, 0 and label the tick marks on the time axis 5, 10, 15, and 20 respectively. Then I draw
vertical dotted lines, extending my time axis tick marks up and down the page through all the
graphs. They all share the same times and this helps me ensure that the graphs relate properly to
each other. In the following diagram we have the axes and the graph. Except for the labeling of
key values I have described my work in a series of notes. To follow my work, please read the
numbered notes, in order, from 1 to 10.
1 How does one remember what goes on which axis? Here’s a mnemonic that applies to all “y vs. x” graphs. See
that “v” in “vs.”? Yes, it is really the first letter of the word “versus”, but you should think of it as standing for
“vertical.” The physical quantity that is closer to the “v” in “vs.” gets plotted along the vertical axis. For instance, in a graph of Position vs. Time, the Position is plotted along the vertical axis (a.k.a. the y-axis) leaving the Time for the horizontal axis (a.k.a. the x-axis). Incidentally, the word mnemonic means “memory device”, a trick, word,
jingle, or image that one can use to help remember something. One more thing: You probably know this, but just in
case: “a.k.a.” stands for “also known as.”
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