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**Distance, Speed and Time Graphs**

What kind of motion happens when an object rolls down a hill?

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**The distance (position) vs. time graph**

Motion graphs are an important tool used to show the relationships between distance, speed, and time. A runner can learn more about performance by studying data and graphs.

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**The distance vs. time graph**

Distance vs. time data tells you the runner’s distance at different points in time. The runner is at 50 meters after 10 sec., 100 meters after 20 sec. and 150 meters at 30 sec.

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**Graphs show relationships**

A good way to show a relationship between two variables is to use a graph. A graph makes it easy to see if changes in one variable cause changes in the other variable (the effect).

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**3.2 The distance vs. time graph**

To graph data, you put distance on the vertical (y) axis . Time goes on the horizontal (x) axis. Data are plotted between x and y axis.

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Reading a graph A graph can give you an accurate answer even without doing the experiment. Students doing an experiment measured the speed of the car at 20, 40, 60, and 80 cm positions. They want to know the speed at 50 cm.

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Slope You can use distance vs. time graphs to quickly compare the speeds of different objects. A steeper line on a distance vs. time graph means a faster speed.

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**Distance vs. time graphs**

The distance vs. time graph has distance on the y-axis and time on the x-axis. Which runner has the fastest constant speed?

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**Speed vs. time graphs These graphs each show the same event.**

What differences do you notice?

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**Do these graphs display the same data?**

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