Note: All graphs should be completed using a pencil and a ruler where appropriate. The following table will be used for our example.
Every graph needs:
Obtaining Information from a Graph
- A title, which is used to describe the graph. This title is usually written as "y" versus "x".
A good title would be: Distance Traveled versus Time.
- An independent variable is set by the experimenter. It is the variable that is intentionally changed and is plotted on the horizontal x-axis.
Time is the independent variable since the experimenter chose its intervals.
- Dependent variable responds to the independent variable. It is the measured or observed value and is plotted on the vertical y-axis.
Distance is the dependent variable since it was measured at each predetermined time interval.
- Each axis must be labeled with a name, symbol (if appropriate), and a unit.
The x-axis would be labeled: Time t (s)
The y-axis would be labeled: Distance d (m)
- Each axis must have an appropriate scale. The scale should be such that the graph is generally one half a page in size. Each division on the axis must be equal and should represent a whole number.
X-axis scale: 4 blocks represents 1 second.
Y-axis scale: 1 block represents 1 meter.
- Plot each point with a dot. Draw a small circle around the dot. This circle helps to locate the dot when a line of best fit has been drawn and it reminds us that all measured points have some error.
- Draw a line of best fit. This line will indicate the trend of a set of points. The line can be curved or it can be straight. If the best fit line is curved it should be drawn freehand. If the best fit is straight use a ruler. Either way do not play Connect-The-Dots. Your best fit will occur when most of the dots are on the line and the rest of the dots are evenly distributed above and below the best fit line.
- Interpolation is when you find a value between measured points. Interpolation involves some error since assumptions (i.e. best fit line) are made.
At 2.5 s, what would be the distance traveled?
The distance traveled would be 4.5 m.
- Locate 2.5 s on the x-axis.
- Draw a line perpendicular to the x-axis until it hits the line of best fit.
- Draw a line from this point perpendicular to the y-axis.
- The point where your perpendicular line intersects the y-axis is your answer.
- Extrapolation is when you find a value before or after a set of measured points. Extrapolation may not be very accurate since you are assuming the trend continues outside the boundaries of your data points.
At what time would the object have traveled 16 m?
The object traveled 16 m in 8.75s.
- Extend the best fit line.
- Locate 16 m on the y-axis.
- Draw a line perpendicular to the y-axis until it hits the line of best fit.
- Draw a line from this point perpendicular to the x-axis.
- The point where your perpendicular line intersects the x-axis is your answer.
- Slope is defined as the rise over the run.
Slope can only be used with a straight line. You can pick any two convenient points on the line as points and . Slope can give you some very important information. When calculating slope it is important to remember your units.
For a distance versus time graph, the slope will be equal to the average speed of the object.
- Error Involved - If all points are close to the best fit line then there is little error involved. The more your points are scattered the more error present. If an individual point is far away from the line then a serious error could have occurred and this point should be remeasured if possible.