 Describing motion along a line

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# 2.5 A note on graph drawing

There will be many occasions throughout your study of physics when you will need to draw graphs. This subsection gives some important guidelines for this activity.

1. Decide which is the independent variable and which the dependent variable. Plot the independent variable along the horizontal axis and the dependent variable along the vertical axis. This is purely a convention but is why, for instance, we usually plot the time along the horizontal axis of a position-time graph. It is the position that varies with time rather than the time that varies with position. Time is the independent variable since we can choose to make a measurement at any time. Position is the dependent variable.

2. Give the graph a title, e.g. distance versus time.

3. Arrange the axes so that the vertical axis increases in an upward direction and values along the horizontal axis increase to the right. This is simply a convention.

4. Label both axes to show which quantities are being plotted and include the units. By convention only pure numbers are plotted. The physical quantity must be divided by its units before being plotted. This means that each axis should be labelled as quantity/units. This is why in all the graphs we have drawn so far the axes have been labelled by time/s and position/m (or displacement/m).

5. Fill as much of the graph paper as reasonably possible. You will obtain greater accuracy if the graph is as big as possible. However, take care to use the graph paper sensibly. Graph paper usually has centimetre and millimetre squares, so it is straightforward to use 2 or 5 or 10 divisions on the paper to one physical unit. What you should avoid are multiples such as 3, 6, 7 ….

6. Scale the axes appropriately, especially if the numbers involved are either very large or very small. For example, if the values of time t range from 0 s to 1.0 × 10﻿−5 s, then, rather than plotting t/s and inserting values such as 1.0 × 10−6, 2.0 × 10−6, etc. along the axis, it is usually more convenient to change the units to microseconds and plot t/μs; the values along the axis will then simply be 1, 2, 3, etc. It is also acceptable to label the axis t/10−6 s rather than t/μs if you prefer.

7. Plot the points clearly. If you use very small dots they may be confused with other marks on the paper. However, using very big dots is not a good idea since it is hard to tell the position of the centre. Some authors put the dots within small circles. In this course we simply use dots since it is easy to show them clearly in professionally drawn graphs.

8. Draw a straight line or smooth curve through the points plotted. The graphs that you draw will generally represent the smooth variation of one quantity with respect to another so a smooth curve is usually appropriate.

## Question 6

How many of the above guidelines did you violate in answering Question 5?

### Answer

Only you will know the answer to this, but it is common to see graphs in which the axes have not been labelled, or the units have been omitted. This is especially true when automated graph-plotting packages are used; such packages often require special instructions if they are to show labels and units, and these are easily overlooked. If you are using such a package (or a graphical calculator), don't forget that the line you have to plot is far from being the whole graph: axes and labels are also important.

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