page 1 graphical analysis of motion by: mike maloney

Graphical Analysis Graphical Analysis of Motionof Motion

By Mike Maloney

Mike Maloney copy 2004Page 2

Graphing MotionGraphing Motion

bull A common way in physics to describe different phenomena is with graphs Scientists often take data plot the data and they analyze the shape of the graph to try to determine relationships between things

bull Our first goal this year will be to identify describe and analyze motion using graphical techniques


Position vs Time (s vs t)Position vs Time (s vs t)

bull One way to graphically describe the motion of an object is to plot a graph of its Position vs Time

bull It is common practice to put Time on the horizontal-axis of a graph

bull So we will put Position on the vertical-axis

bull A position vs time graph may look something like this hellip


s vs ts vs t


s vs ts vs t

bull From this graph we can tell a few things about the motion of our object

bull First we can tell the position of the object at any point in time by reading it off the graph

bull If the graph increases the object moves in the (+) direction

bull If the graph decreases the object moves in the (-) direction

bull What does it mean if the graph goes into the negativesndash The position is negative or you might say you are

behind what you called the ldquo0rdquo position


Interpreting an ldquos vs trdquoInterpreting an ldquos vs trdquo

Now letrsquos can see what ldquos vs trdquo plots tell us about motion



We know that we can read the position of an object directly from a ldquos vs trdquo plot



bull At 15 seconds where is the objectbull Between 8 and 9 meters



We can also determine the change in position by reading values from the graph



How far does it move from 1 to 3 seconds



bull How far does it move from 1 to 3 secondss = 14 ndash 5 = 9 meters

9


Slope of ldquos vs trdquoSlope of ldquos vs trdquo

Now letrsquos try do determine some not so easy to see data from our ldquos vs trdquo plot



bull How do you find the slope of a linebull change in y change in x


ldquoldquos vs trdquos vs trdquo

bull So what would the slope of a ldquos vs trdquo plot give usbull change in y change in xbull change in s change in t or s tbull the rate of change of position or the velocity


So far hellip (s vs t)So far hellip (s vs t)bull A position vs time plot tells us the position (s) of an

object at any point in timebull It can either be positive or negative

bull Positive (+) positive of where you startedbull Negative (-) negative of where you started

bull The change in ldquoyrdquo on a position vs time plot from one point to another gives us the displacement (s)

bull Going Up (+change) moving in the positive directionbull Going Down (-change) moving in the negative directionbull The slope of the position vs time plot tells us the velocity


Velocity vs Time (v vs t)Velocity vs Time (v vs t)

bull Another way to graphically describe motion is to make a plot of the velocity of an object versus time

bull Again we will put Time on the horizontal-axis and Velocity on the vertical-axis

bull A plot of a velocity vs time graph may look like this hellip


v vs tv vs t

Velocity vs Time

-10 ms

-8 ms

-6 ms

-4 ms

-2 ms

0 ms

2 ms

4 ms

6 ms

8 ms

10 ms

0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s


v vs tv vs t

From this graph we can tell the velocity of an object at any point in time


v vs tv vs t

Notice that this graph has points both positive and negative


v vs tv vs t

bull What does the positive part of the graph indicatebull The times when the velocity was positive or when the

object was moving in the positive direction


v vs tv vs t

bull What about the negative part of the plotbull The times when the velocity was negative or the

object was moving in the negative direction


v vs tv vs t

As the plot increases in the positive direction the speed of the object increases


v vs tv vs t

As it goes down in the positive part of the graph the speed of the object decreases


v vs tv vs t

As the plot goes down in the negative section the speed also increases but in a negative direction


v vs tv vs t

This would be symbolic of increasing a carrsquos speed in reverse


v vs tv vs t

As the plot goes up in the negative section the speed decreases in the negative direction


v vs tv vs t

This would be symbolic of slowing down in reverse


Speed and VelocitySpeed and Velocity

bull This brings up a common confusion in physics hellip why do we have speed and velocity

bull Speed is just the number part or the size of the velocity it is what the speedometer in you car reads

bull Velocity not only tells you how fast but also in what direction you are going


So far hellip (v vs t)So far hellip (v vs t)bull A velocity vs time plot tells us the velocity of an


bull Positive (+) velocity [+direction]bull Negative (-) velocity [-direction]

bull Going Up (+part) increasing positive speed velocity goes upbull Going Down (+part) decreasing positive speed velocity goes downbull Going Up (-part) decreasing negative speed velocity goes upbull Going Down (-part) increasing negative speed velocity goes down


v v

s tv v

s t

bull So we can read the velocity of an object directly off the chart


bull Like in other graphs we can also talk about its slope

bull What is the slope of a ldquov vs trdquo graph

v v

s tv v

s t


bull Slope = change in y change in xbull = change in velocity change in

timebull Slope = v t = acceleration

v v

s tv v

s t


bull The area underneath the curve gives us something also

bull How would we find the area underneath the curve from 1 sec to 3 sec

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

time (s)

velo

city

(m

s)

v v

s tv v

s t


bull Area = height x base= velocity x change in time

bull Area = v tbull that is the equation for displacement (s)

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

time (s)

velo

city

(m

s)

v v

s tv v

s t


a vs ta vs t

bull We can extrapolate our ideas on position and velocity graphs to acceleration vs time plots

bull The Area under the curve in an a-t graph is ndash (Acceleration) (time)ndash a tndash Which is change in velocity (v)

bull The slope (at) actually gives us something called the jerk but we donrsquot have to worry about that in this class


In ConclusionIn Conclusion

bull Slope of ldquos vs trdquo plot is velocitybull Slope of ldquov vs trdquo plot is

accelerationbull Area under ldquov vs trdquo plot is

displacementbull Area under ldquoa vs trdquo plot is

velocitybull Now lets try some hellip

Graphical Analysis of Motion

Mike Maloney copy 2004

Graphing MotionGraphing Motion

bull A common way in physics to describe different phenomena is with graphs Scientists often take data plot the data and they analyze the shape of the graph to try to determine relationships between things

bull Our first goal this year will be to identify describe and analyze motion using graphical techniques








s vs ts vs t


s vs ts vs t

























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v vs tv vs t

Velocity vs Time

-10 ms

-8 ms

-6 ms

-4 ms

-2 ms

0 ms

2 ms

4 ms

6 ms

8 ms

10 ms

0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s


v vs tv vs t



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v v

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0 1 2 3 4 5 6 7

time (s)

velo

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(m

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time (s)

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v vs tv vs t

Velocity vs Time

-10 ms

-8 ms

-6 ms

-4 ms

-2 ms

0 ms

2 ms

4 ms

6 ms

8 ms

10 ms

0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s


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velo

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v vs tv vs t

Velocity vs Time

-10 ms

-8 ms

-6 ms

-4 ms

-2 ms

0 ms

2 ms

4 ms

6 ms

8 ms

10 ms

0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s


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time (s)

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time (s)

velo

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(m

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v vs tv vs t

Velocity vs Time

-10 ms

-8 ms

-6 ms

-4 ms

-2 ms

0 ms

2 ms

4 ms

6 ms

8 ms

10 ms

0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s


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time (s)

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v v

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time (s)

velo

city

(m

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a vs ta vs t
































v vs tv vs t

Velocity vs Time

-10 ms

-8 ms

-6 ms

-4 ms

-2 ms

0 ms

2 ms

4 ms

6 ms

8 ms

10 ms

0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s


v vs tv vs t



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time (s)

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a vs ta vs t











page 1 graphical analysis of motion by: mike maloney

Documents

mike maloneymike maloney

position s

time s

tmike maloney

xmike maloney

velocitymike maloney

s change

slope of s