Student-centred approaches to introducing kinematics to high school students

1. ZAME Annual Provincial Conference
7-8 July, 2014
Christian Kasumo, MSc, MBA, BSc, Dip Ed

2. Introduction
What is kinematics?
What should be taught?
How should it be taught?
Conclusion
Acknowledgements
2

3.  Kinematics plays a very important
role in everyday life, be it on a
sports field, at a rocket launch or
racetrack; calculation of speed is
the most important factor.
 Kinematics is an important tool in
understanding the motion of
objects, whether translational,
oscillatory, or circular.
3

4.  The behaviour of variables
such as speed, velocity,
acceleration, and deceleration
is described by the equations
of motion.
 In addition to the equations,
some other tools for studying
kinematics are graphs,
diagrams and vectors.
4

5. Velocity-time (v-t) graphs
and displacement-time (or
distance-time) (x-t) graphs
relate equations of motion
in a very simple way.
5

6.  Kinematics is the study of objects
in motion.
 The terms used most frequently in
kinematics are speed, velocity,
acceleration, time, distance and
displacement. As we define these
physical quantities, we must
emphasise whether they are scalar
or vector quantities.
6

7.  Scalar Quantities: These are
physical quantities fully described
only by a magnitude and not a
direction (e.g., distance,
temperature, area, volume, speeds,
etc.).
7

8. For example, the
temperature on a cold
windy day is 5 degrees
Celsius (only magnitude) or
the distance travelled by a
child from home to school
is 2 km (only magnitude).
8

9.  Vector Quantities: These are
physical quantities fully
described by both a
magnitude and a direction
(e.g., displacement, velocity,
acceleration, force and
momentum).
9

10. Distance: Length covered
during the motion of an
object (measured in
metres). It is a scalar
quantity. For example, a
boy walks from school to
his home and covers 800m
so distance is 800m.
1
0

11.  Displacement: This is the
shortest distance between
the point of origin and the
point of termination. Thus
displacement involves both
direction and magnitude
(and is therefore a vector
quantity). It is measured in
metres.
11

12.  A physics teacher walks 4m East, 2m
South, 4m West, and finally 2m North.
 What is the distance covered by the
teacher? _____ m
 What is his/her displacement? _____ m
12
4m
4m
2m2m

13.  Speed: The ratio of the total
distance travelled to the time
interval. It is the rate at
which an object covers
distance. Speed is a scalar
quantity and is measured in
miles/hour (mph),
kilometres/hour (km/h) or
meters/second (m/s).
13

14.  Velocity: The speed of an object in
a specific direction is called the
velocity. It is the displacement
per unit time, so it is the rate at
which an object changes its
position. As the displacement is
in metres and time is in seconds,
the units for velocity are metres
per second (m/s). Velocity is a
vector quantity.
14

15.  Sometimes the velocity over a
long period is also called
average velocity. Average
velocity is the average of all
instantaneous velocities.
Usually motor vehicle speeds
are expressed as average
speeds, i.e. total distance
travelled/total time taken.
15

16.  The velocity of an object at a
particular instant of time is the
instantaneous velocity.
According to the definition of
average velocity, if d1 and d2 are
two positions of an object at time
t1 and t2 respectively, then
average velocity = (d2–d1)/Δt or
d2=d1+average velocity x Δt is
the equation of motion.
16

17.  This equation allows us to find
the position of an object after
the lapse of time Δt when the
original position is other than
the origin.
17

18. Slope of the line on a position-time graph
is equal to the velocity of the object
18
t
x
v




19.  Acceleration: This is the rate of
change of velocity per unit time.
 Acceleration is a vector quantity
and is measured in m/s2
 For example, if an object is moving
with a velocity of 5.0 m/s and it
changes its velocity to 7.5 m/s in
5.0 seconds, then acceleration of
object is a = change in velocity/
time taken = (7.5–5.0)/5 = 0.5
m/s2
19

20. 20
Positive Velocity
Zero Acceleration
Positive Velocity
Positive Acceleration
Slope of the line on a velocity-time
graph is equal to the acceleration of
the object
t
v
a




21.  Sometimes the change in the
velocity is due to decrease in
velocity that leads to
negative acceleration called
deceleration or retardation
 The definition of acceleration
gives the very first equation
of motion in kinematics
21

22. 22

23.  Teaching must begin with the
definitions given above so that
learners are able to distinguish
the concepts
 Then teach the kinematic
equations: Given an initial
velocity u, a final velocity v, a
displacement d, an acceleration
a and a time t
23

24. (a)
(b)
(c)
(d)
24
2
2
1
atutd 
t
vu
d
2


atuv 
aduv 222


25. If an object is in free fall, the
equations of motion can be
applied as follows:
 An object in free fall
experiences an acceleration of
-9.8 m/s2. The - sign indicates
a downward acceleration.
Whether explicitly stated or not,
the value of the acceleration in
the kinematic equations is -9.8
m/s2 for any freely falling
object.
25

26. If an object is merely
dropped (as opposed to
being thrown) from an
elevated height, then the
initial velocity of the object
is 0 m/s.
26

27.  If an object is projected upwards in
a perfectly vertical direction, then it
will slow down as it rises upward.
The instant at which it reaches the
peak of its trajectory, its velocity is
0 m/s. This value can be used as
one of the motion parameters in the
kinematic equations; for example,
the final velocity (v) after traveling
to the peak would be assigned a
value of 0 m/s.
27

28.  If an object is projected upwards in
a perfectly vertical direction, then
the velocity at which it is projected
is equal in magnitude and opposite
in sign to the velocity that it has
when it returns to the same height.
That is, a ball projected vertically
with an upward velocity of +30
m/s will have a downward velocity
of -30 m/s when it returns to the
same height.
28

29. We begin by noting some
common student difficulties:
 Differentiating the concepts of
position, velocity and acceleration
 Making, using and interpreting
graphs with time as the variable
plotted on the x-axis
 Kinematics has too many
formulae and calculations
29

30. Mathematics, the language
of physics, is not every
learner’s cup of tea
Recognizing the difference
between average and
instantaneous velocity
30

31. Separating slope from path
of motion.
Interpreting changes in
height and changes in
slope (e.g., Is the object
slowing down? Which
motion is slowest?)
31

32.  Understanding the physical
significance of the sign of a
body's velocity
 Understanding that it is
possible to have zero velocity
and non-zero acceleration,
or non-zero velocity and
zero acceleration
32

33.  Understanding that the
direction of acceleration
relative to velocity determines
whether an object speeds up
or slows down
 Understanding that a body can
have a positive velocity and
negative acceleration (or the
reverse) simultaneously
33

34. How can we as teachers help
learners to overcome these
difficulties?
 Teach basic kinematics concepts
by connecting them with real life
situations (e.g., sports field and
race track etc.)
 Give students examples requiring
them to substitute values in linear
and quadratic equations.
34

35. Once they are familiar with
substituting values of
different variables, give
them assignments on
equations of motion.
35

36.  To further strengthen
students’ skills, organize them
into teams or groups in which
they can carry out classroom
activities on collecting,
graphing and analyzing data,
and assess them on the basis
of cooperative learning.
36

37.  At the end of the derivation of
each equation of motion,
provide students with a
worksheet based on that
equation and assess them
individually.
37

38.  Encouraging students to work
towards common goals
increases achievement,
improves attitudes towards
minorities and those with
disabilities and increases
inclusion in mainstream
classroom activities.
 Teach kinematics content
through classroom interaction.
38

39.  To strengthen skills in reading
technical terms, get students to
read numerical problems in
class.
 After reading problems, students
should recognize the different
terms or data in the problems.
 Each student should then select
the equation of motion according
to the data he/she has collected.
39

40.  For example, an athlete who starts
running from rest position completes a
100m race in 12.5 seconds. What is his
acceleration?
 The athlete started from the rest, so
initial velocity (u=0); completes the
race in 12.5 seconds (t=12.5 seconds);
and distance travelled or displacement
(d=100m) and the requirement is the
acceleration a
 So, given a mathematical model, to the
problem, u=0; t=12.5; s=100; a=?
40

41.  Teach kinematics in a learner-centred
way.
 Involve the learner as much as possible.
 Help the learner to discover the kinematic
ideas through interacting with real life
situations.
 Teach the learner how to substitute values
into formulae and how to evaluate.
 Explore activities that can be used to
encourage active learning on the part of
the learner.
 Explore use of software (e.g., Geogebra).
41

42. I wish to thank:
 The organisers of this conference
for the invitation to facilitate
here and interact with colleagues
 Mulungushi University for
funding my participation in this
conference
 You all for listening.
42

43. Husty, M. L. (not dated), Using Geogebra in
Elementary Geometry, Institut für Grundlagen der
Bauingenieurwissenschaften, AB Geometrie and CAD,
Universität Innsbruck, Austria
Kaulu, G. (2008), Effectiveness of the
‘PhysicsClassroom’ Computer Software in the
Learning of Kinematics at Munali Boys High School in
Lusaka, MEd Dissertation, University of Zambia,
Lusaka
Leonard, W. J. and Gerace, W. J. (1999), A
Demonstration of Kinematic Principles, University of
Massacussetts Physics Education Research Group
Wadhwa, K. L. (2007), Kinematics (Equations of
Motion), University City High School
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44. THE END
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