Motion Graphs Lecture 3

Video14. Bill Nye: Motion

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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

Video15. Graphing Motion

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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

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

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

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

Video16. Position vs Time

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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.

Steeper Line = Faster Speed

Steeper Line = Faster Speed

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.

Basically…

You might want to draw thisgraph in your Motion MathLittle book

This is another really good graph to draw in yourmotion math little book

Video 17. Distance, Velocity &

Acceleration

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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

Does your graph look like this?Be sure you have this one drawn

• 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

Predict: What does Predict: What does THIS GRAPH show?THIS GRAPH show?

• 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..

Speed Vs. TimeSpeed Vs. Time• Used to show an

object’s speed at a given time.

• Speed: on y-axis• Time: on x-axis

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.

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!

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)

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

Video 18. PUTTING IT ALL TOGETHER

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