distance vs. time - tecumseh local school district 3_5.pdf · distance vs. time graph describing a...
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Distance vs. Time
Analysis of a
Distance vs. Time Graph
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What can the motion on a
Distance (d) vs. Time (t) Graph
Where did the object start?
Which direction did it go?
Where did the object stop?
Is the motion uniform (constant)?
Is the motion non-uniform (changing)?
Can you tell which is faster? (if 2 or more objects are
present)
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Distance vs. Time Graph
Describing a journey made by an object is not exciting 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. Let's look a closer look:
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Distance Time Graph
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.
Distance runs vertically (the y-axis).
The higher up the graph we go, the further we are from
the start.
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The slope of a line on a distance-time graph is speed
The steeper the slope, the faster you are traveling
The flatter the slope, the slower you are traveling
Graphing Motion
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Not moving? This is what it looks like…
If something is not moving, a horizontal line is drawn in a
distance-time graph
Time is increasing to the right, but its distance does not
change. It is stationary.
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Moving….
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. It moves at a steady speed.
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Can you describe what is going on here?
First part : Steady (slow) speed
Second part: Increase in speed (Covering a much larger distance in the same time.)
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What are the three parts to the journey shown below:
Moving at a steady speed (slowly)
Not moving for quite some time
Moving again, but at higher speed
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Example #1
Each line (A and B) represent the motion of two objects. Which object
is moving faster? Explain.
Graphing Motion
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Example #2
Which car has a faster speed: The big car or small car? Explain
Graphing Motion
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Example #3
Using this graph, what is the average speed of the Big Car
and the average speed of the small car?
Graphing Motion
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Different Motion Graph Examples
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What is the slope of a distance vs. time graph?
Speed!!!
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What is the speed of the airplane?
Phoenix
Denver
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Rise=?
3 hours
600 m
Speed = Slope = Rise/
Rise/
What is the speed of the airplane?
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Different Slopes
0
1
2
3
4
5
6
7
8
1 2 3 4 5 6 7
Time (hr)
Dis
tan
ce (
km
)
Run = 1 hr
Run = 1 hr
Run = 1 hr
Rise = 0 km
Rise = 2 km
Rise = 1 km
Slope = Rise/Run
= 1 km/1 hr
= 1 km/hr
Slope = Rise/Run
= 0 km/1 hr
= 0 km/hr
Slope = Rise/Run
= 2 km/1 hr
= 2 km/hr
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Question
• Below is a distance vs. time graph of my position
during a race. What was my AVERAGE speed for
the entire race?
0
2
4
6
8
10
12
14
0 1 2 3 4 5 6
Time (hr)
Dis
tan
ce (k
m)
Average Speed = Total distance/Total time = 12 km/6 hr
= 2 km/hr
Run = 6 hr
Rise = 12 km
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Question
Below is a distance vs. time graph for 3 runners. Who
is the fastest?
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 35
Time (h)
Dis
tan
ce (
mi.)
Bob
Jane
Leroy
Leroy is the fastest. He completed the race in 3 hours
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Here is another time-distance graph with 2 journeys represented on the same graph.
Each line represents a journey from home to the office.
The red line is Dave’s journey.
The green line is Mike’s journey.
1000 m
500 m
0 5 10 15
D
i
s
t
a
n
c
e
Time (min)
How long after Dave does Mike
leave?
3 min
After how many minutes does
Mike catch up?
7 min
How far from home are they
then?
Dave: 71.66 m/min
Mike: 100 m/min
What is the speed of each
person?
500 m
1500 m
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Question #4
What is going on in each section of the following distance-time
graph?
3.5 Assessment Questions
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3.5 Homework
• Graphing “Little Dudes I”
• Graphing “Little Dudes II”
• Little Dots in Uniform Motion