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GRAPHING MOTION Distance vs. Time

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GRAPHING MOTION Describing a journey made by an object is very boring if you just use words. As with much of science, graphs are more revealing. Plotting distance against time can tell you a lot about a journey.

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GRAPHING MOTION Let's look at the axes:

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GRAPHING MOTION Time always runs horizontally (the x-axis). The arrow shows the direction of time. The further to the right, the longer time from the start.

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GRAPHING MOTION Distance runs vertically (the y-axis). The higher up the graph we go, the further we are from the start.

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GRAPHING MOTION If something is not moving, a horizontal line is drawn on a distance-time graph. Time is increasing to the right, but its distance does not change. This graph shows an object that is stationary.

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GRAPHING MOTION If something is moving at a steady speed, it means we expect the same increase in distance in a given time. Time is increasing to the right, and distance is increasing steadily with time.

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GRAPHING MOTION This graph shows an object that moves at a steady, constant speed.

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GRAPHING MOTION Both the lines below show that each object moved the same distance, but the steeper yellow line got there before the other one. What does this indicate?

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GRAPHING MOTION A steeper slope indicates a larger distance moved in a given time. In other words, higher speed. This is shown in yellow.

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**GRAPHING MOTION Yellow: speed = distance / time = 30 m / 10 s = 3 m/s**

Blue: speed = distance / time = 20 m / 20 s = 1 m/s

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GRAPHING MOTION For the first part of the journey shown by the graph below, the object moved at a steady (slow) speed.

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GRAPHING MOTION Then the object suddenly increased its speed, covering a much larger distance in the same time. The speed increased in the second part of the journey.

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GRAPHING MOTION The line below is curving upwards. This shows an increase in speed, since the slope is getting steeper over time.

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GRAPHING MOTION In other words, in a given time, the distance the object moves is larger. It is accelerating.

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**GRAPHING MOTION Stopped? Moving at a quick constant speed?**

There are three parts to the journey shown here… Where is the graph showing motion that is: Stopped? Moving at a quick constant speed? Traveling at a slow constant speed? C B A

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**GRAPHING MOTION Stage 1: 100 m in 10 s. Stage 2: 50 m in 10 s.**

The graph below shows several stages of motion: Stage 1: 100 m in 10 s. Stage 2: 50 m in 10 s. Stage 3: 150 m in 20 s. Calculate the speeds of each stage, indicated by the colors.

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**GRAPHING MOTION The graph below shows several stages of motion:**

Stage 1: speed = distance / time = 100 m / 10 s = 10 m/s Stage 2: speed = distance / time = 50 m / 10 s = 5 m/s Stage 3: speed = distance / time = 150 m / 20 s = 7.5 m/s.

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**GRAPHING MOTION The graph below shows several stages of motion:**

Stage 1: constant speed at a relatively high rate Stage 2: constant speed at a relatively slow rate Stage 3: constant speed at a “medium” rate (between the others)

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**GRAPHING MOTION The graph below shows several stages of motion:**

The slope of the line (its steepness) indicates rate of change of position. Speed can be estimated by the slope of the line… faster, slower, etc.

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GRAPHING MOTION Distance vs. time graphs also indicate the position of the object. Stage 1 & Stage 2: object is moving away from the starting point Stage 3: object is moving back toward the starting point (it comes back to zero)

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GRAPHING MOTION The steeper the line on a distance vs. time graph, the faster the object’s speed. A curved line indicates a change in speed (accelerating or decelerating).

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GRAPHING MOTION Lines pointing up indicate moving away from the starting location. Lines pointing down indicate moving back towards the starting location.

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**GRAPHING MOTION Let’s see how much this makes sense to you…**

This is not for a grade, just to let me know how much of this and what parts of it you “get.”

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**GRAPHING MOTION To learn about speed vs. time graphs, visit this link:**

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