Implementation of Scientific Method in
Treatment Theme Accelerated Motion
- Final paper -
Mentor:
Student:
Ph. D. Dušanka Obadović, full prof.
Zouhor Zekri
Novi Sad, 2012
UNIVERSITY OF NOVI SAD
FACULTY OF SCIENCES
DEPARTMENT OF PHYSICS
4
2. Theory of Accelerated Motion
First we will give the definition of acceleration and write the basis of accelerated motion.
Average and instantaneous acceleration can be defined.
2.1. Average and Instantaneous Acceleration
As a particle moves from one point to another along some path, its instantaneous velocity
vector changes from
i
v
at time
i
t
to
f
v
at time
f
t
. Knowing the velocity at these points
allows us to determine the average acceleration of the particle:
The average acceleration of a particle as it moves from one position to another is defined
as the change in the instantaneous velocity vector
v
divided by the time
t
during which
that change occurred:
t
v
t
t
v
v
a
i
f
i
f
(2.1)
Figure 2.1 A car, modeled as a particle; moving
along the x axis from A to B has velocity
xi
v
at
i
t
t
and velocity
xf
v
at
f
t
t
.
Graph 2.1 Velocity-time graph (rust) for particle
moving in a straight line. The slope of the blue
straight line connecting A and B is the average
acceleration in the time interval
i
f
t
t
t
.
Because it is the ratio of a vector quantity
v
and a scalar quantity
t
, we conclude that
average acceleration is a vector quantity directed along
v
. As indicated in Figure 2, the
direction of
v
is found by adding the vector
i
v
(the negative of
i
v
) to the vector
f
v
,
because by definition
i
f
v
v
v
When the average acceleration of a particle changes
during different time intervals, it is useful to define its instantaneous acceleration a:
The instantaneous acceleration
a
is defined as the limiting value of the ratio
t
v
as
t
approaches zero:
dt
v
d
t
v
a
t
lim
0
(2.2)
In other words, the instantaneous acceleration equals the derivative of the velocity vector
with respect to time.
5
It is important to recognize that various changes can occur when a particle accelerates.
First, the magnitude of the velocity vector (the speed) may change with time as in straight-
line (one-dimensional) motion. Second, the direction of the velocity vector may change
with time even if its magnitude (speed) remains constant, as in curved-path (two-
dimensional) motion. Finally, both the magnitude and the direction of the velocity vector
may change simultaneously.
2.2. Uniformly Accelerated Motion
in Straight Line (Linear)
Uniform (constant) acceleration motion is a type of motion in the velocity of an object
changes by an equal amount in equal time period.
Graph 2.2 Acceleration-time graph for uniformly accelerated motion in straight line
Due to the unique algebraic properties of constant acceleration, mathematicians have
derived formulae:
(2.3)
(2.4)
(2.5)
Graph 2.3 Velocity-time graph for uniformly accelerated motion in straight line
Graph 2.4 Displacement-time graph for uniformly accelerated motion in straight line
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3. Methodology
A common misconception in science is that science provides facts or "truth" about a
subject. Science is not collection of facts; rather, it is a process of investigation into the
natural world and the knowledge generated through that process. This process of
investigation is often referred to as the scientific method and it is typically defined in many
textbooks and science courses as a linear set of steps through which a scientist moves
from observation through experimentation and to a conclusion as shown below:
Figure 3.1 Science is not a linear process
However, this classic portrayal has a number of problems. Science is not a linear process
– it doesn’t have to start with an observation or a question, and it commonly does not even
involve experiments. Instead, the scientific method is a much more dynamic and robust
process (Figure 1). Scientists get their inspiration from the natural world, from reading
what others have done, from talking to colleagues, or from experience. They use multiple
types of research toward investigating phenomena, including experimentation, description,
comparison, and modeling. Some scientific investigations employ one of these methods,
but many involve multiple methods, or some studies may even have characteristics of
more than one method. Results from one research study may lead in directions not
originally anticipated, or even in multiple directions as different scientists pursue areas of
interest to them.
Inquiry-based Learning and Scientific Method in Schools
Importance of inquiry is great because memorizing facts and information is not the most
important skill in today's world. (Facts change, and information is readily available - what's
needed is an understanding of how to get and make sense of the mass of data.)
Infants begin to make sense of the world by inquiring. The process of inquiring begins with
gathering information and data through applying the human senses - seeing, hearing,
touching, tasting, and smelling.
An old adage states: "Tell me and I forget, show me and I remember, involve me and I
understand." The last part of this statement is the essence of inquiry-based learning.
"Inquiry" is defined as "a seeking for truth, information, or knowledge - seeking information
by questioning."
Key principles of inquiry learning are those listed here:
1. All learning activities should focus on using information-processing skills (from
observations to synthesis) and applying the discipline "ground rules" as a means to
learn content set in a broad conceptual context.
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