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Motion Graphs Lecture 3
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Motion & GraphsMotion & Graphs• Motion graphs are an important tool used
to show the relationships between position, speed, and time.
• It’s an easy way to see how speed or position changes over time
• These types of graphs are called kinematic graphs.
• There are two types:– Position vs. Time graphs– Speed vs. Time Graphs
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Position Vs. TimePosition Vs. Time• Used to show an
object’s position at a given time.
• Position: on y-axis• Time: on x-axis
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You Try It: You Try It: Graphing Position Graphing Position
Vs. TimeVs. Time• Suppose you are helping a friend who is training for a track meet.
• She wants to know if she is running at constant speed.
• You mark the track in 50-meter increments and measure her time at each position during a practice run.
• Create a position-time graph using her data.
Time (s)
Position (m)
0 0
10 50
20 100
30 150
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You Try It: You Try It: Graphing Position Graphing Position
Vs. TimeVs. Time• When you’ve plotted all 4
points, you should get a graph that looks like this…
• What would her speed be?– Choose any point, &
divide distance (position) over time
Time (s)
Position (m)
0 0
10 50
20 100
30 150
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You Try It: You Try It: Graphing Position Graphing Position
Vs. TimeVs. Time• What would her speed be?
– 50m/10s = 5 m/s– 100m/20s = 5 m/s
• Notice that this is a straight line - why??– She is moving at a constant
speed - neither slowing down nor accelerating
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You Try It: You Try It: Graphing Position Graphing Position
Vs. Time #2Vs. Time #2• Graph the motion of this car.
• Graph the points: (0,0), (1, 10), (2, 20), (3, 30), (4, 40), (5, 50).• Your graph should look like this…
• What is this car’s velocity?– A constant 10 m/s
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What does slope What does slope have to do with it?have to do with it?
• Slope is the ratio of the rise (y-axis) to the run (x-axis) of a line on a graph.
• A bigger slope means a steeper line which means a faster speed.
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Steeper Line = Faster Speed
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Steeper Line = Faster Speed
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Negative SlopesNegative Slopes• What does this graph
mean??? • And this one?• They show an object that is
slowing down - or decelerating.
• The first graph is slowly decelerating, while the second graph is quickly decelerating.
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Basically…
You might want to draw thisgraph in your Motion MathLittle book
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This is another really good graph to draw in yourmotion math little book
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• Now consider a car that has a changing Now consider a car that has a changing velocity.velocity.
• It is not moving at a constant rate, but It is not moving at a constant rate, but getting faster by the second.getting faster by the second.
• What would this graph look like?What would this graph look like?• You try it firstYou try it first……
Position Vs. Time - Position Vs. Time - Changing VelocityChanging Velocity
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Does your graph look like this?Be sure you have this one drawn
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• What would the graph look like for a car that traveled 10 m in the 1st second, 15 m by the 2nd second, 25 by the 3rd second, and 40 m by the 4th second?
You Try It: You Try It: GrAPHING GrAPHING
Position Vs. Time #3Position Vs. Time #3
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Predict: What does Predict: What does THIS GRAPH show?THIS GRAPH show?
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• This graph is for a car This graph is for a car moving with a constant moving with a constant velocity of +5 m/s for 5 velocity of +5 m/s for 5 seconds, stopping seconds, stopping abruptly, and then abruptly, and then remaining at rest for 5 remaining at rest for 5 seconds.seconds.
• The straight line means its The straight line means its position is position is NOT changingNOT changing..
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Speed Vs. TimeSpeed Vs. Time• Used to show an
object’s speed at a given time.
• Speed: on y-axis• Time: on x-axis
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Speed Vs. Time - Speed Vs. Time - Constant SpeedConstant Speed
• This graph shows the speed versus time for a ball rolling at constant speed on a level floor.
• On a speed vs. time graph, constant speed is shown with a straight horizontal line.
• If you look at the speed on the y-axis, you see that the ball is moving at 1 m/s for the entire 10 seconds.
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Speed Vs. Time - Speed Vs. Time - Constant SpeedConstant Speed
• Compare this speed-time graph to the position-time graph for the ball.
• Both of the graphs show the exact same motion, even though they look different.
• If you calculate the slope of the lower graph, you will find that it is still 1 m/s.
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You Try It: Graphing You Try It: Graphing Speed Position Vs. Speed Position Vs.
TimeTime• Maria walks at a constant speed of 6 m/s for 5 seconds.• Then, she runs at a constant speed of 10 m/s for 5 seconds.• Create a speed-time graph using her data.
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Speed Vs. Time - Speed Vs. Time - Changing SpeedChanging Speed
• As we know, most objects don’t move at a constant speed.
• If a speed vs. time graph slopes up, then the speed is increasing.
• If it slopes down, then the speed is decreasing.
• If the graph is horizontal, then the object is moving at a constant speed.YOU MAY WANT TO DRAW THESE GRAPHS TOO!
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Putting it All Together
1. Which runner won the race?– Albert won the race. He
reached 100 meters first.
2. Which runner stopped for a rest?– Charlie stopped for a rest
at 50m.
3. How long did he stop for?– Charlie stopped for 5
seconds. (13-8)
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Putting it All Together
4. How long did Bob take to complete the race?– Bob finished the race in
14 seconds
5. Calculate Albert's average speed.– Speed = distance/time– Speed = 100m/12s = – Albert’s Speed = 8.3
m/s