TIMS Laboratory Investigations
Velocity and Acceleration
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(ISBN 0-7872-4120-2, intermediate & middle): The goal of the investigation is to have the children understand that velocity is a compound variable made up of a displacement, D, and a time interval, Dt . In the investigation we slowly work up to a full understanding of velocity as v = D/Dt, first by holding one, then the other of the two variables fixed and then allowing both variables to change. The children hop, crawl, skip, or run races over either a fixed distance (Part I) or for a fixed time (Part II). In each part D vs. Dt is plotted for all the activities on the same graph and the association made between the speed of the racer and the steepness of the curve. Starting with an intuitive understanding of velocity in each part and relating this to the graphical results, we proceed from the idea of common denominators (fixed time) and common numerators (fixed displacements) to a full-blown proportional reasoning—formal operational understanding of velocity when both distance and time can vary.
A Changing Velocity I: A Qualitative Look at Acceleration
(ISBN 0-7872-4121-0, middle): A cart with a water clock is rolled
down a ramp, and the pattern of drops is analyzed. The children
note that the time interval between drops, Dt, is constant but that the spacing between drops, D, continuously
increases. Comparing these results with their experiences in A
Day at the Races, the children determine that the velocity of
the cart must be continuously increasing. We then qualitatively
define acceleration, and the children explore this definition
through the various drip patterns, and graphically through their
D vs. Dt plot, which is not a straight line, once again confirming that
velocity of the cart is not constant, hence accelerating. Finally,
the children find the algebraic relationship D vs. Dt by straightening out the curve. The lab provides an early, qualitative
introduction to acceleration.
Free Fall I
(ISBN 0-7872-4122-9, middle): In Part I of the investigation,
using the full force of gravity, a 1-inch sphere is dropped from
heights of 1 m, 2 m, and 3 m while the falling time, Dt, is recorded. As in A Changing Velocity I, the D vs. Dt curve is not a straight line. Following in the footsteps of
similar relationships, the children straighten out the curve.
In Part II the children investigate to see whether mass, shape,
or size of the falling object affects their results. Some surprises
are in order. The questions focus on whether the sphere is accelerating,
how they know, whether all falling objects have the same acceleration,
and finally some analytical problems using their newly discovered
equation of motion for a freely falling object.
Motion down a Ramp: Average vs. Instantaneous Velocity
(ISBN 0-7872-4123-7, middle): The major goal of this investigation
is to find the relationship between the instantaneous velocity
of an object, v, and the time t as it rolls down an incline. The
children should already know how to calculate the average velocity
<v> of an object over a distance d and time t. Unfortunately,
there is no easy way to measure an object’s velocity at an instant.
In Part I the children find the relationship between the <v> and
v for the special case of a sphere rolling from rest down an incline
by determining <v> on the incline and its final “instantaneous”
velocity after it leaves the incline. By changing the starting
position of the sphere, the children can plot a curve of <v> vs.
v and find the surprisingly simple relationship. In Part II we
challenge the children to use what they have learned in Part I
to find the instantaneous velocity of the water cart at any instant
on the incline for the condition that it is released from rest.
The children then use this v vs. t data to make graphical and
analytical predictions, and then combine the v vs. t results with
their definition of average velocity to solve multistep problems
relating v, t, and d.
What’s Average about the Average Velocity?
(ISBN 0-7872-4124-5, middle): The children once again use the
incline and water cart and what they have learned in previous
velocity investigations to determine the cart’s velocity vs. time
curve on the incline. The children then use the data to find the
time in each interval at which the instantaneous velocity has
the same value as the average velocity. Finally, the children
generalize their results and show how the average velocity over
an interval of time is related to the instantaneous velocities
at the beginning and the end of that interval. The children are
then challenged with a variety of problems involving initial velocities,
final velocities, displacements, and time intervals that sharpen
their skills in solving multistep logic problems.
A Changing Velocity II: A Quantitative Look at Acceleration
(ISBN 0-7872-4125-3, middle): In this investigation, the children
explore the quantitative definition of average acceleration. Before
beginning the investigation, we try to lead the children to the
correct definition of <a> = Dv/Dt. The children load up their water cart, tilt the long incline,
and from the water marks determine the cart’s average velocity
versus time. The children then use the results from Average vs.
Instantaneous Velocity to find the instantaneous velocity of the
cart vs. time. This is plotted and the acceleration determined
from the slope of the straight line curve. Then, there are questions
galore, as we generalize from a cart to a sphere, think about
steeper inclines, and solve basic problems both graphically and
analytically involving acceleration, Dv, and Dt as unknowns in all possible combinations. Using multistep logic
and thinking about signs representing directions are also part
of the lab. If the children stick to it, this lab should accelerate
their learning.
Bull’s-Eye II: All in Good Time
(ISBN 0-7872-4126-1, middle): This will be our second look at
projectile motion. Bull’s-Eye I was our first. In Bull’s-Eye II,
we will study the relationship between the horizontal launch velocity
of our projectile, vL, and the distance it lands from the edge of the table, d. We
will also look at the relationship between the time the projectile
is in the air, Dtair, and d. The surprising result will allow the children to find
d for any table height, something that we could not do in Bull’s-Eye
I. We have designed Bull’s-Eye II as a year-end assessment lab.
The children will be expected to use what they have learned in
previous investigations to find vL. We also expect them to draw pictures, set up data tables, pick
the values of the manipulated variable, plot their results, make
and check predictions, solve general problems, and make up problems
of their own. The lab is a blend of learning new ideas and recalling
old ones, all in good time.
Free Fall II: A g Whiz
(ISBN 0-7872-4127-X, middle): In Free Fall II, we ask the children
to “design and carry out an experiment to find the velocity vs.
time curve for a freely falling object and determine its acceleration.”
The investigation is open-ended to the extent that there are no
hints on how to proceed nor a data table with any information
filled in. However, we expect the students to use the fundamental
definition of acceleration that they learned in A Quantitative
Look at Acceleration and the same technique for finding ag. We ask them to find the class average of ag and compare this to the standard value and answer some very challenging
questions, including several involving multistep logic. Before
they start the investigation, we want to make sure the children
can distinguish up from down. This will be the first time that
we have attempted to give the displacement a sign. Based on this,
the children see what happens when an object is thrown up in the
air as well as dropped, not only on the Earth but on the moon
as well. If the children can do all of this, then each will truly
be a g whiz.
Acceleration vs. Shape
(ISBN 0-7872-4128-8, middle): One of the wild, wacky, and wonderful
things about acceleration is that if you drop objects of different
masses and shapes, they all have the same acceleration. But when
you roll them down an incline, things are not so simple. It is
the acceleration of rolling objects we are going to explore in
Acceleration vs. Shape. We are going to treat this as an open-ended
assessment lab. This means we keep the student lab instructions
to a minimum, pose questions both analytical and experimental,
and let the children use their skills as scientists to come to
two general conclusions—that when an object rolls down an incline
its acceleration does not depend upon its mass but it does depend
upon its shape. The children will use spheres, solid cylinders,
and cylindrical rings and determine the acceleration for each.
They will race them down the incline in pairs, first predicting
and then determining which will win and by how much. We will even
try handicapping races to make them come out a tie. A fun lab.
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Copyright © 1997 by Kendall/Hunt Publishing Company
Copyright © 1999 Institute for Mathematics and Science Education.
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UIC—University of Illinois at Chicago