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Position-Time Graphs:
Position versus time graphs represent changes which occur in an object's position with respect to time. The slope of the line is the velocity (change in position divided by the change in time) of the object.
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Many students of physics have acquired shortcutitis. The ailment often shows its ugly head on a question like this. The common mistake is to pick a single point on the line and simply calculate the ratio of the y to x coordinate for the point. But don't be fooled! The slope is not the ratio y/x; it is the ratio y/x. Two coordinate points must be known and the change of each coordinate calculated. So find two x-y coordinate points for the line on the graph and follow the surecut method described in the Math Magic section. Then remind yourself that surecuts are often shorter than shortcuts.
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The task of determining the slope of the line on a graph involves:
- Pick two points on the line and determine their x-y coordinates. It is critical to select points whose coordinates are clearly known and not simply guessed at.
- Based on the coordinates of these two points, determine the amount of rise of the line between the two points. The rise is the change in the y-coordinate for the line as it stretches from the first selected point to the last point.
- Determine the amount of run of the line between the two points. The run is the change in the x-coordinate for the line as it stretches from the first selected point to the last point.
- Calculate the ratio of rise to run: slope rise/run.
- Check the sign on your slope value to insure its accuracy. A downward sloping line has a negative slope.
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The Minds On Physics program calculates answers accurate to the fourth decimal place. Your answer does not need to be that accurate. The program will allow you to have a deviation of approximately 0.05 from the right answer without being wrong. This means you should enter your answer to at least the second decimal place.
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