Walk this Way – Graphing Motion Activity
Introduction
A rate is defined as some quantity divided by a time interval. For motion, the most common rate would
be called velocity (commonly known as speed in one direction); it is defined as the ratio of the distance
traveled divided by the time interval taken to do the traveling.
velocity =
distance traveled
time interval
or → v =
d
t
From this definition you can also work backward. If you know the rate, or velocity, as well as the time
interval traveled, you can easily find the distance traveled using:
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distance traveled = velocity × time interval
or → d = v t
Strictly, the rate defined above is the average velocity (average speed traveled during the time interval –
the actual speed at any instant may have been different).
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Another rate we will be interested in when studying motion will be our rate change of velocity – this is
known as acceleration:
acceleration =
change in velocity
change in time interval
or → a =
Δv
Δt
In other words, acceleration is the rate that you are changing your velocity (rate of going faster, slower, or
turning).
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Graphing Motion
We can make a picture of our motion using 3 types of graphs (distance vs. time, velocity vs. time, and
acceleration vs. time graphs). There are a just a few things to remember when viewing these graphs.
• On a distance vs. time graph:
- If the graph moves up you are moving one direction, if it goes down you are moving in the
opposite direction.
- If the graph is flat you are at the same distance, thus: you are not moving.
- If the graph has a constant diagonal slope – you are moving at a constant speed (velocity).
- If the graph curves – you are accelerating (changing your velocity –> for positive direction curving up = faster, curving down = slower).
Δy
Δd
=
= velocity .
- The slope of this graph = the velocity of the motion -> slope =
Δx
Δt
• On a velocity vs. time graph:
- A flat line = a constant velocity (moving but moving at the same speed, say 2 m/s).
- A line moving away from zero is going faster (+ graph = one direction, - graph = opposite).
€ are accelerating (up slope = faster, down slope
- A diagonal line = changing your velocity = you
= slower (for positive direction)).
Δv
- The slope of this graph = the acceleration of the motion -> a =
Δt
- Summing the area under the curve = the distance travel by that time -> d = v t .
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Let’s see what this all means by looking at a few motion graphs of simple motion. Below are the distance
vs. time, velocity vs. time, and acceleration vs. time graphs for the basic forms of motion.
On the distance vs. time graph:
Notice the 3 different shapes of the graph
for 3 different types of motion.
• Squares represent -> standing still at 5 m
away.
• Clear circles represent -> moving at a
constant velocity of 2 m/s.
• Filled circles show -> motion moving
faster & faster – smoothly accelerating.
___________________________________
On the velocity vs. time graph:
• Squares represent -> standing still, thus
velocity = 0
• Clear circles represent -> moving at a
constant velocity of 2 m/s, a constant/flat
line. The area under that line forms a box,
area = 2m/s x 5s = 10m = distance at 5s.
• Filled circles show -> motion moving
faster (0 -> 5m/s) –accelerating (a = 1 m/s2,
i.e. the slope = 1 m/s2. The area under that
line forms a triangle, area = .5 x base x ht =
.5 x 5s x 5m/s = distance at 5s = 12,5 m.
______________________________________
On the acceleration vs. time graph:
• Squares represent -> standing still, v = 0,
change in v = 0, thus a = 0 m/s2.
• Clear circles represent (not seen in graph
behind squares) -> moving at a constant velocity
of 2 m/s –> thus change in v = 0 -> a = 0.
• Filled circles show -> motion moving faster
(0 ->5m/s) –> accelerating (a = 1 m/s2 constant).
The area under that line forms a box, area = 1
m/s2 x 5s = velocity at 5s -> 5 m/s.
Walk this way Activity / Competition
Objective:
• Collect distance and velocity versus time information for a walker by matching predetermined graphs using a
motion detector & computer.
• Determine the velocity versus time graph from a distance versus time graph.
• Determine distances moved by a walker from their velocity versus time graph.
Procedure: the motion detector a computer will be set-up for you.
-
-
You will be divided into groups by your instructor.
Think about what you are about the do and clearly map out a plan before you start each part.
Follow the instructions below for each part.
Goto: Applications -> Logger Pro 3 -> Physics with Computers -> 01a Graph Matching.xmbl and open that file.
Case 1: make a position vs. time graph – standing still for 2 sec
-> then moving away at a constant v = 1 m/s for 3 sec.
-
Place the motion detector on the edge of a table pointing to an open area. Think about how you will
make this graph.
After a few minutes your teacher will select (at random) a “walker” and a “talker” from your group who
will carry out the experiment (so everyone in your group must understand the task).
Prepare to walk away from the detector at a uniform pace, starting at a distance of about 1 meter.
When you are ready: the “talker” will click on “collect” in the toolbar or press F11 to start and give the
“walker” hints on how and when to move (the “walker” should not be able to see the screen).
The teacher will count down the time (3, 2, 1 – start) and all groups should start at the same time.
After the graphs are made, the instructor will each graph and award a point to the group with most
accurate graph.
Case 2: Match the given position vs. time graph
Open file: 01b Graph Matching.xmbl
- Your group has about 5 min to decide what you must do to exactly reproduce the graph on the
screen by walking in front of the motion detector.
- You will do the same as above (case 1) to match the graph – teacher awards 1 point for best match.
Part II:
- Your group sits at there seat and draws a velocity versus time graph of the distance versus time
graph they just matched – teacher awards 1 point for first group with the correct graph (must include
the exact numbers and units).
Case 3: Match the next position vs. time graph
Open file: 01c Graph Matching.xmbl
- Your group has about 5 min to decide what you must do to exactly reproduce the graph on the
screen.
- You will do the same as above to match the graph – teacher awards 1 point for best match.
Case 3: Match a velocity vs. time graph
Open file: 01d Graph Matching.xmbl
- Your group has about 5 min to decide what you must do to exactly reproduce the graph on the
screen. Remember this speed not distance.
- You will do the same as above to match the graph – teacher awards 1 point for best match.
Part II:
- Your group sits at their seat and draws the distance versus time graph of the graph they just matched
– teacher awards 1 point for first group with the correct.
Part III:
- Your group sits and draws acceleration versus time graph of the distance & velocity versus time
graph they just drew – teacher awards 1 point for first group with the correct graph.