Table of Contents

Module 2: Understanding Motion Graphs

Unit 1: Distance-Time Graphs (Slope)

A Graph Study

 

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A typical distance-time graph is shown to the left.

The straight line represents the motion of an object moving at constant velocity.

The curved line represents the motion of an object whose speed is increasing.

In general, finding the slope on a d-t graph will yield the object's velocity.

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Slope is defined as the ratio of rise/run (i.e. slope = rise/run) between two points.

On a d-t graph, where the axes have units of metres and seconds, the slope has units of m/s, which is of course, speed.

Finding the slope of a straight line is fairly simple, because the slope is constant.

For a curved line, there is no unique slope. When the slope is taken between two arbitrary points A to B, the slope is called the average speed between the two points.

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To find the slope at a single point C, on a curved line, one must first use a ruler to draw a tangent to the curve (at the designated point).

Doing this graphically "by eye" gives surprisingly accurate results, if done carefully.

The graph to the left shows how one would determine the speed of the object at point C.

Note that the values one uses for both rise and run at point C will usually be different for every person who draws the tangent line... but the slope (i.e. the ratio of rise/run) will always be the same, or at least very similar.

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