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Distance vs. Time

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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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Let's look at the axes:

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

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

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

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

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

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

16. 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

17. 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.

18. 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.

19. 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)

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

24. 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.”

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