Attached is the pdf

Revised 12/9/07

Name_____________________________________ Period_________ Date_________

CONCEPTUAL PHYSICS Experiment

4.7 Linear Motion: Motion Graphs

GO! GO! GO!

Purpose

In this experiment, you will plot a graph that represents the motion of an object.

Required Equipment and Supplies

constant velocity toy car

butcher paper (or continuous—unperforated—paper towel, or equivalent)

access to tape

stopwatch

meterstick

graph paper

Discussion

Sometimes two quantities are related to each other, and the relationship is easy to see. Sometimes

the relationship is harder to see. In either case, a graph of the two quantities often reveals the

nature of the relationship. In this experiment, we will plot a graph that represents the motion of a

real object.

Procedure

We are going to observe the motion of the toy car. By keeping

track of its position relative to time, we will be able to make a

graph representing its motion. To do this, we will let the car run

along a length of butcher paper. At one-second intervals, we

will mark the position of the car. This will result in several

ordered pairs of data—positions at corresponding times. We

can then plot these ordered pairs to make a graph representing

the motion of the car.

Step 1: Fasten the butcher paper to the top of your table. It should be as flat as possible—no hills

or ripples.

Step 2: If the speed of the toy car is adjustable, set it to the slow setting.

Step 3: Aim the car so that it will run the length of your table. Turn it on and give it a few trial

runs to check the alignment.

Step 4: Practice using the stopwatch. For this experiment, the stopwatch operator needs to call

out something like, “Go!” at each one-second interval. Try it to get a sense of the one-second

rhythm.

Step 5: Practice the task.

a. Aim the car to drive across the length of the butcher paper and let it go.

b. After it starts, the stopwatch operator will start the stopwatch and say, “Go!”

c. Another person in the group should practice marking the location of the front or back of

the car on the butcher paper every time the watch operator says, “Go!” For the practice

run, simply touch the eraser of the pencil to the butcher paper at the appropriate points.

d. The watch operator continues to call out, “Go!” once each second and the marker

continues to practice marking the location of the car until the car reaches the end of the

butcher paper or table. Take care to keep the car from running off the table!

Thanx to

Dean Baird

Go! Go! Go! page 2 of 4

Step 6: Perform the task.

a. Aim the car to drive across the length of the butcher paper and let it go.

b. After it starts, the stopwatch operator will start the stopwatch and say, “Go!”

c. Another person in the group will mark the location of the front or back of the car on the

butcher paper every time the watch operator says, “Go!” No marks are to be made on the

paper until the car is moving.

d. The watch operator continues to call out, “Go!” once each second and the marker

continues to mark the location of the car until the car reaches the end of the butcher paper

or table. Take care to keep the car from running off the table!

Step 7: Label the marked points. The first mark is labeled “0,” the second is labeled “1,” the third

is “2,” and so on. These labels represent the time at which the mark was made.

Step 8: Measure the distances—in centimeters—of each point from the point labeled “0.” (The

“0” point is 0 cm from itself.) Record the distances on the data table. Don’t worry if you don’t

have as many data points as there are spaces available on the data table.

Data Table

Time

t (s) 0 1 2 3 4

Position

x (cm) 0

Step 9: Make a plot of position vs. time on the

graph paper. Title the graph “Position vs. Time.”

Make the horizontal axis time and the vertical axis

position. Label the horizontal axis with

the quantity’s symbol and the units of measure: “t

(s)”. Label the vertical axis in a similar manner.

Make a scale on both axes starting at 0 and

extending far enough so that all your data will fit

within the graph. Don’t necessarily make each

square equal to 1 second or 1 centimeter. Make the

scale so the data will fill the maximum area of

the graph.

We could just as easily make a graph of time vs.

position. But we prefer position vs. time for a few

reasons. In this experiment, time is what we call an

“independent variable.” That is, no matter how fast

or slow our car was, we always marked its position

at equal time intervals. We were in charge of the

time intervals; the car was “in charge” of the

change in position it made in each interval. But the

change in position of the car in each interval

depended on the time interval we chose. So we call

position the “dependent variable.” We generally

arrange a graph so that the horizontal axis

represents the independent variable and the vertical

axis represents the dependent variable. Also, the

slope of a position vs. time graph tells us more than

the slope of a time vs. position, as we will see later.

Step 10: Draw a line of best fit. In this case, the line of best fit should be a single, straight line.

Use a ruler or straight edge; place it across your data points so that your line will pass as close as

possible to all your data points. The line may pass above some points and below others. Don’t

simply draw a line connecting the first point to the last point. An example is shown in Figure 1.

Figure 1

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100

90

80

70

60

50

40

30

20

10

0

0 1 2 3 4 5 6

t (s)

x

(c

m

)

Position vs. Time

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•

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Step 11: Determine the slope of the line. Slope is often referred to as “rise over run.” To

determine the slope of your line, proceed as follows.

a. Pick two convenient points on your line.

They should be pretty far from each other.

Convenient points are those that intersect

grid lines on the graph paper.

b. Extend a horizontal line to the right of the

lower convenient point, and extend a

vertical line downward from the upper

convenient point until you have a triangle

as shown in Figure 2. It will be a right

triangle, since the horizontal and vertical

lines meet at a right angle.

c. Find the length of the horizontal line on

your graph. This is the “run.” Don’t use a

ruler; the length must be expressed in units

of the quantity on the horizontal axis. In

this case, seconds of time.

Run: ____________________ s

d. Measure the length of the vertical line.

This is the “rise.” Don’t use a ruler; the

length must be expressed in units of the

quantity on the vertical axis. In this case,

centimeters of distance.

Rise: ____________________ cm

e. Calculate the slope by dividing the rise by the run. Show your calculation in the space

below.

Slope: ___________________ cm/s

Summing Up

1. Suppose a faster car were used in this experiment. What would have been different about

a. the distance between the marks on the butcher paper?

b. the number of seconds the car would have spent on the butcher paper before reaching the

edge?

c. the resulting distance vs. time graph? (How would the slope have been different?)

2. Add a line to your graph that represents a faster car. Label it appropriately.

3. Suppose a slower car were used in this experiment. What would have been different about

Figure 2

.

100

90

80

70

60

50

40

30

20

10

0

0 1 2 3 4 5 6

t (s)

x

(c

m

)

Position vs. Time

•

•

•

•

•

Run

R

is

e

Go! Go! Go! page 4 of 4

a. the distance between the marks on the butcher paper?

b. the number of seconds the car would have spent on the butcher paper before reaching the

edge?

c. the resulting distance vs. time graph? (How would the slope have been different?)

4. Add a line to your graph that represents a slower car. Label it appropriately.

5. Suppose the car’s battery ran out during the run so that the car slowly came to a stop.

a. What would happen to the space between marks as the car slowed down?

b. Add a line to your graph that represents a car slowing down. Label it appropriately.

6. What motions do these graphs represent?

In other words, what was the car doing to

generate these motion graphs?

Line A.

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Line B.

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