LAB 1: INTRODUCTION TO MOTION

Position 

Name: 

Date: ___________Partners: ________________ 

________________ 

LAB 1: INTRODUCTION TO MOTION 

Time 

OBJECTIVES 

After completing this lab you should be able to: 

OVERVIEW 

Describe in words the motion of an object, given its position-time graph 

Draw a position-time graph of an object from a description in words of the motion 

Draw the velocity-time graph when given a position-time graph, and the reverse 

Draw initial and final position vectors for an object, given its position-time graph 

Draw an object’s final position vector, given its initial position and displacement 

Determine the velocity of an object from data taken from the position-time graph 

Determine an object’s displacement, given a portion of its velocity-time graph 

The motion of an object can be described in words, as a graph, by vector diagrams, or by a 

mathematical equation. This lab will concentrate on describing an object’s motion in words 

and graphs, for constant velocities. You will also learn to translate the description from one 

form to the other. You will use a computerized sonic range-finder to plot position-time graphs 

of your motion, or your lab partner’s motion. The sonic range-finder requires that you move 

in a fairly straight line, either toward or away from the detector. This week we will try to 

move at steady speeds, slow or fast. One lab partner must log in – don’t forget to log out! 

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Lab 1: Uniform Motion 

INVESTIGATION 1: POSITION-TIME GRAPHS 

Activity 1-1: Producing Position-Time Graphs as You Move 

The purpose of this activity is to learn how to relate graphs of position versus time to the 

motions they represent. 

You will need Pasco’s Data Studio software, CI-750 Interface and a Motion detector. You 

will also need a two-meter stick or tape on floor placed at one meter intervals. 

Representing location: The meter stick is a portion of a coordinate system that extends in 

both directions. The range-finder is at the origin of this coordinate system, with its speaker 

aimed along the positive x –axis. At any instant in time objects can occupy various locations 

on that axis. Unless otherwise stated, the units on all axes will be in meters. 

Motion 

detector 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 

In the diagram above, the professor has position x = +2 m, and the wolf has x = – 5 m. 

The range-finder is at the “origin” x = 0 m, so all locations are measured from (relative to) it. 

An object’s location is represented by an arrow from the origin to the object : tail at origin, tip 

at object. Because the orientation of the arrow matters, this is called the position “vector”. 

On the diagram above, draw the location vector for the wolf, and also draw the position vector 

for the prof. Note that the range-finder cannot detect echoes from objects behind it (unlike the 

professor), so you will not encounter negative positions in this lab’s data. You may encounter 

them in homework questions however. As you walk or run along the x–axis, your distance 

from the range-finder is determined (by timing the reflected “click”), and the graph on the 

computer screen will display your position at each instant in time, measured from the origin. 

Procedure: 

1. Log in to the computer. Open the 202Labs folder with a DOUBLE CLICK on the folder icon; 

then open the Lab 1 folder. Load Activity 1-1 into the DataStudio application by dragging the 

Activity icon onto the DataStudio icon. 

2. Begin graphing positions by clicking the green [START] button at the top left. Verify that 

the range-finder measures positions correctly, by standing still at a measured distance from it. 

Describe the shape of the position-time graph you obtain: ____________________________. 

Make sure the detector is measuring correctly before you continue. 

The sonic ranger gives the position of the nearest object that makes an echo, so it will give the 

position of anyone who crosses the straight-line path between you and the detector. If you are 

not in the path of the (focused) sound wave, it might detect the distant wall. Try standing at x 

= 2 m, but swinging your arms as if walking. It will not correctly measure objects closer than 

½ meter, so don’t make graphs at close distances. 

3. Now move away and towards the motion detector at different speeds until you understand 

the different shapes of the position-time graphs. Discuss your understanding with your lab 

partners until you all agree. How is a slow speed indicated on the location-time graph? Fast 

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Position (m) 

Position (m) 

Position (m) 

Position (m) 


speed? What does the graph look like when you move toward the detector? Away from it? 

Note it is better to use the terms away and towards, rather than forward and backward, since 

the latter might be confused with the walker’s orientation as they move. After completing this 

activity you should be able to look at a distance-time graph and describe the motion of an 

object. You should also be able to look at the motion of an object and sketch a graph 

representing that motion. The next step is to give you some practice in doing this. 

4. On the axes below, predict the shape of the position-time graphs for each of the described 

motions with a broken line. Then check your predictions by moving in the described way and 

draw the actual curve with a solid line. 

a. Use broken line first predict a distancetime 

graph, walking away from the 

detector (origin) slowly and steadily. 

Now check your prediction and draw it 

with a solid line. 

b. Use broken line first predict a distancetime 


detector (origin) medium fast and steadily. 

Now check your prediction and draw it 

with a solid line. 

Time (s) 

c. Use broken line first predict a distancetime 

graph, walking toward the detector 

(origin) slowly and steadily. Now check 

your prediction and draw it with a solid 

line. 

Time (s) 

d. Use broken line first predict a distancetime 


detector (origin) starting off medium fast 

and slowing down to a stop. Now check 

your prediction and draw it with a solid 

line. 

Time (s) 

Time (s) 

Question 1-1: What is the difference between the graph made by walking away from the 

detector slowly and steadily and the one made walking away quickly and steadily? 

Question 1-2: What is the difference between the graph made by walking steadily toward the 

motion detector and one made walking steadily away from the motion detector? 

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Question 1-3: What is the difference between the graph made by walking away from the 

detector at constant speed and one where the person walks away but slows down? 

Activity 1-2: Describing and Matching Position-Time Graphs of Your Motion 

By now you might be pretty good at predicting the shapes of a position-time graph. But can 

you do things the other way around? Can you read a position-time graph, and figure out what 

motions would reproduce it? You will describe the desired motion in words, then test your 

description by moving that way, to see how well your graph matches the original graph. 

Procedure: 

1. Open the experiment file L1A1-2a. A position-time graph similar to this will appear. 

2. Describe how you would move to produce this graph 

3. Now move in front of the motion sensor so as to match the graph on the computer screen. 

Each partner should try a turn at this. Teamwork! Get the times right; get the distances right! 

Question 1-4: What was the difference in the speed in the differently sloped parts of the 

graph, a-b, b-c and c-d? 

Question 1-5: What was the difference in the direction in the differently sloped parts of the 

graph, b-c and c-d? 

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INVESTIGATION 2: MEASURING DISPLACEMENT 

The velocity of an object is defined as the rate of change in position. So it is important to 

understand how change in position is measured. The change of position is given by the 

difference in the final and initial coordinates, or x f - x i , and is called the displacement. You 

will see that displacement is a quantity that has both magnitude, or size, and direction. Such 

quantities are common in physics, and are called vector quantities. Vector quantities are often 

given bold type. 

Representing Displacement: Let’s revisit the wolf and the professor - both have undergone 

a displacement since we last looked. An arrow drawn from the initial position to the final 

position can be used to represent the displacement of each. 

x 

Motion Detector 

x 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 

The symbol , Delta, is usually used to denote “change in__”. So the displacements are: 

x prof = x f - x i = (4) - (2) = +2m 

x wolf = x f - x i = _________________ 

Because of the choice of positive and negative x values, x f >x i for both the professor and the 

wolf, so both displacements are positive. Note that the wolf first moves towards the origin 

(motion detector) and then away, but it has a positive velocity throughout! Since the motion 

detector detects objects on the positive x-axis only, detector motion away from the detector is 

always positive and moving towards is always negative. For an object or person on the 

negative x-axis this is not the case. For example the wolf in the above diagram, moves 

towards and then away from the origin, but is moving in the positive x direction throughout. 

Examine the diagram to confirm this statement. Now figure out how you could move towards 

then away from the origin and be moving in the –x direction throughout. 

Activity 2-1: Drawing Vector Diagrams 

Vector Representation and Vector Diagrams: The change in position of the Prof. can be 

illustrated in a vector diagram where “arrows” drawn to scale represent the initial and final 

positions, and also the change in position. Adding the change in position vector to the initial 

position vector gives the final position vector. Mathematically: 

Procedure: 

x = x f - x i so x f = x i + x 

1. Vector Diagram. Examine the vector representation of the initial. x i , and final position, x f , 

of the professor relative to the origin in the diagram below. Note that vector arrows that 

start at the origin are used to represent the initial and final positions in a vector diagram. A 

point on the x-axis is not sufficient. 

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2. In a vector diagram where there is a change in position, there must also be a displacement 

vector arrow x which when added “head–to-tail” to the initial position vector, x i , must 

give the final position vector, x f . In the vector diagram above, draw the change in position 

vector. It should agree with x drawn in the diagram of the professor on the previous 

page. 

Does the displacement vector you have drawn above, x, agree with the displacement 

vector of the professor drawn in the above diagram of the professor and the wolf? 

3. The situation for the displacement of the wolf is a little more complicated, since its initial 

position is in the negative direction, but once again x i and x added head-to-tail give x f . 

Vector Diagram. Add a displacement vector arrow x to the initial position vector so that 

it gives the final position of the wolf. 

Does it agree with displacement vector of the wolf drawn in the above diagram of the wolf 

chasing the professor? 

4. From this it is clear that the direction of the change in position for both the Prof. and the 

wolf are both in the positive x direction. For that reason both velocities are positive. 

5. What if the motion is in the opposite direction? In the situation shown below, calculate the 

displacement of the lady and her dog in the short time since the leash was pulled out of 

her hand. 

x 

x 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 

Substitute initial and final positions into the equations below to get x. 

x lady = x f - x i = _______________ 

x dog = x f - x i = _______________ 

6. You will notice that both displacements in this case are in the negative x direction. Does 

this agree with the sign of the displacements calculated above? Explain. 

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Velocity (m/s) 


7. Draw vector diagrams for the lady to obtain the displacement vector. First draw the initial 

and final position vectors, and then draw the displacement vector. Make sure your result 

corresponds to the x lady in the diagram above. Do the same for the lady’s dog. 

Vector diagram for lady 

8. 

Origin 

Vector diagram for dog 

Origin 

Measuring Velocity: Velocity is defined as the change in position, or displacement, divided 

by the change in time. 

Just like the displacement, velocity has magnitude and direction and is a vector quantity. 

Thus, when the displacement is positive, x f >x i , the velocity is positive. If x f


can walk steadily without the sudden changes of speed that occur as you push off with one 

foot and then stop with the other. 

3. Check your prediction using the motion detector. Make sure you are already moving 

slowly and steadily when you start to record so that you don’t record the motion as you speed 

up from a standing start. We will look at that motion later on. Repeat until you get a graph 

you're satisfied with. Note that it is difficult to obtain a smooth line since you don’t really 

move smoothly when you walk, so ignore the smaller bumps that are mostly due to your 

steps. You will get a smoother graph if you shuffle rather than taking big steps. 

4. On the same set of axes, predict the velocity-time graph you will get walking in the 

positive x direction medium fast and steadily. Check your prediction. 

5. On the same set of axes, predict the velocity-time graph you will get walking in the 

negative x direction medium fast and steadily. Check your prediction. 

Question 2-1: What is the most important difference between the velocity-time graph made 

by walking slowly and one made by walking away more quickly? 

Question 2-2: How are the velocity-time graphs different for motion in the positive x 

direction and the negative x direction? 

Question 2-3: Can you tell, from a velocity-time graph, your position when you started 

walking and where you were when you stopped walking? Explain. 

Activity 2-3: Position-Time and Velocity-Time Graphs of the Same Motion 

Prediction: Using a dashed line draw the position-time and velocity-time graphs you would 

expect if you were to: 

1. walk away from the detector slowly and steadily for about 5 seconds, then 

2. stand still for about 5 seconds and then 

3. walk toward the detector steadily about twice as fast as before 

Once again, assume you can walk steadily without sudden changes of speed as you push 

off with one foot and then stop with the other. 

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Compare your predictions and see if you can all agree. 

Procedure: Open the experiment file L1A2-3 and test your prediction. Draw the best graph 

on the axes above using a solid line. Be sure the 5-second stop shows clearly. 

Question 2-4: The velocity is the slope of the position-time graph. Explain how this is 

demonstrated from your graphs. 

Question 2-5: In producing the above velocity-time graph, did it matter where you started i.e. 

your initial position? Did you have any difficulty with walking the full 5s after the stop? 

Explain. 

Measuring the Velocity from the Slope of the Position-Time Graph: As you are now 

aware the position-time graph for an object traveling at constant velocity is a straight line. 

And, as you have observed, the faster you move, the more inclined is your position-time 

graph. The slope of a position-time graph is displacement divided by change in time. It is a 

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Position (X) 

Position (X) 


quantitative measure of this incline, and therefore gives the velocity of the object. 

(t2,x2) 

(x2- x1) 

(t1,x1) v = 

(x2 - x1) 

(t2 – t1) 

Time (t) 

(t2 - t1) 

Note that if the graph slopes downward, then x 2


Results from position-time graph: 

Use the Smart Cursor button, , to read the position and time coordinates on the graph for 

two typical points while you were moving. You will have to drag the cursor to the point that 

you want to measure. For the better accuracy, use two points on the line that are far apart but 

still typical of the motion. These need not be the same points used in measuring the velocity 

directly with a stopwatch, and t 1 ≠ 0s since t =0 when you start recording data with the motion 

sensor. Don’t forget to put in units! 

Measurement 

Position 1 x 1 = 

Position 2 x 2 = 

Data and results 

Displacement x =(x 2 - x i ) = 

Time 1 t 1 = 

Time 2 t 2 = 

Time interval t = (t 2 - t i ) = 

Velocity x / t = 

Question 2-6: Was your displacement positive or negative? Why? Was the velocity positive 

or negative? Is this what you expected from the direction of your motion? Why? 

Question 2-7: Does the velocity you calculated from the position-time graph agree exactly 

with the velocity you calculated directly using the stopwatch? Do you expect them to agree 

exactly? Why? How would you account for any differences? 

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Vector Representation of Velocity: Velocity implies both speed and direction. How fast 

you move is your speed. The rate of change of position with respect to time is velocity which 

may or may not have the same numerical value as speed. As you have seen, for motion along 

a line (e.g., the x axis) the sign (+ or -) of the velocity indicates the direction. If you move in 

the positive x direction your displacement and therefore your velocity is positive. The faster 

you move in the positive x direction, the larger positive number. If you move in the negative x 

direction your displacement and therefore your velocity is negative. The faster you move in 

the negative x direction, the "larger" the negative number. 

These two ideas of direction and speed can be combined and represented by vectors. An 

arrow pointing in the direction of motion represents a velocity vector. A single “tick” is used 

to distinguish it from the displacement vector. The velocity vector is usually drawn above the 

object, and the length of the arrows are drawn in proportional to the velocity at that instant, so 

the greater the velocity the longer the arrow. This can be illustrated for the case of the Wolf 

and the Prof. The wolf moves three times farther than the Prof. in the same time, so has it 

three times the velocity. 

x 

x 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 

Draw the velocity vectors for the lady and her rapidly disappearing dog. You have already 

calculated the displacement in the same time interval, so you know the relative speeds of the 

dog and the lady. The length of the vectors should be approximately in the same ratio as those 

speeds. 

x 

x 

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 

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Conclusion: 

(Approximately 1 page in length. Use Separate sheet of paper.) 

Questions: 

1. In the space provided, describe how you would move to create the following 

position-time graphs. To distinguish between different shapes and slopes, you 

must use the terms moving steadily when the speed is constant and faster or 

slower where there are different the speeds in a single graph. Also use towards 

or away from the detector. Don’t use backwards or forwards since moving 

backwards or forwards while moving away from the detector produces the 

same graph. 

2. Standing on a bridge above an expressway, you noticed that at 4:30pm a truck is 

+350m from the bridge (the origin in your chosen reference frame). At 4:31pm, it is - 

250m on the opposite side of the bridge. Calculate the velocity of the truck. 

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Now from the origin draw vectors to represent both the initial and final positions and a 

vector that gives the displacement vector. 

Does the direction of the vector arrow x agree with the sign of the velocity 

calculated above? Explain. 

3. Use the numerical values on the axes to draw the exact velocity graphs for an 

object whose motion produced the position time graphs shown below on the 

left. Position is in meters and velocity in meters per second. 

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LAB 1: INTRODUCTION TO MOTION

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