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Appendix A
Graphing a Linear Function
Consider an object that is moving at constant velocity v
o
, until at a certain time it
is given a constant acceleration a in the direction of motion. In this case the velocity v at
a later time is given by v = v
o
+ at where t is the time measured from the time of
application of a. (See Chapter 1 of your text). Knowing this fact, suppose you wanted to
investigate experimentally to see if a certain object moving in a straight line was
undergoing constant acceleration. Suppose, further, that to investigate this you made the
following measurements of velocity at various times t.
V (m/s)
t (sec)
7.5
9.8
12.8
16.3
18.8
22.1
24.5
28.2
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Suppose, also, that from studying your experimental arrangement you know that
the time has been measured very accurately, but the measured velocities are uncertain to
±
0.5 cm/s.
How would you decide whether, within experimental error, your measurements
indicate a constant acceleration? Probably the best way would be by plotting a graph of v
versus
t.
While
many
people
use
computers now to make and analyze
such plots, they do so only after they
know how to make and interpret such
plots manually. The purpose of this
appendix is to review your knowledge of
how to plot linear functions such as v =
v
o
+ at. You may have studied linear
functions is the standard form y = mx +
b. For example, you may have plotted y
= 5x + 6 and you may have determined
that such a function yields a straight line
or linear plot with slope m = 5, y
intercept b = 6 and x intercept b/m =
6/5. In any case, plot y = 5x + 6 for
5
1
≤
≤

x
on linear (ordinary) graph
paper and determine
from your graph
the
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slope and x and y intercepts. Remember that the slope is determined by using a section of
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 Fall '09
 LIND
 Physics, Logarithmic scale, Logarithm, 0.5 cm, loglog paper, Linear Paper

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