Kinematics: Combined M
otion
Kinematics is
the science
of motion without regarding its
causes.
There are various possibilities of combining different types
of motions.
On the one hand types of motion
which happen at the same time e.g. a boat
crossing a
river, a hoist lifting a load etc.
On the other hand motions can be combined in a chronological order, for
instance
the
starting of a train,
its
driving at a constant velocity and its
deceleration.
The three types of motion
to be discussed are :

motion
in a straight line with steady velocity

motion in a straight line with constant acceleration

motion in a straight line with constant deceleration
Preconditions
: The definitions of the velocity v and the acceleration a are
known.
Aim
: Description of a
combin
ed motion in diagram form an
d discussion of the
three areas in the sketch.
Ziel
: Darstellung des Bewegungsablaufes
in Diagrammform und D
isku
ssion der
drei Abschnitte in der Skizze.
Time needed
: 3 units
Starting

up questionnaire as a basis for d
iscussion
:
1)
What is the definition of the velocity v?
Which units are used according to the SI

System?
2)
Which types of velocity do you know?
3)
What is the definition of the acceleration a?
Which unit is used according to the SI

System?
4)
What is the number of
the gravitational acceleration g in Austria?
Discussion of the v

t

Diagram
v

t

d
iagram
Area
I
:
Type of motion: motion in straight line with constant accel
eration
.
Given physical quantity
:
a
1.
Calculation of s and v:
2
1
1
1
2
t
a
s
m
1
1
1
*
t
a
v
s
m
Calculation of s and v at any time t:
2
1
)
(
*
2
t
a
s
t
m
t
a
v
t
*
1
)
(
s
m
∆ t
1
t
1
∆ t
2
t
2
∆ t
3
t
3
t[
s
]
V[
m/s
]
v
1
v
2
v
3
I
II
III
v
0
v
E
Area II
:
Type of motion:
motion in a straight line with steady velocity.
Calculation of s and v:
2
2
2
*
t
v
s
m
3
1
2
v
v
v
s
m
Calculation of s and v at any time t:
t
v
s
t
*
2
)
(
m
Area III
:
Type of motion: motion in a straight line with steady deceleration.
Give
n physical quantity:

a
3
Calculation of s and v:
2
3
3
3
3
3
*
2
*
t
a
t
v
s
m
v
E
=O
Calculation of s and v at any time t:
2
3
3
)
(
*
2
*
t
a
t
v
s
t
m
t
a
v
v
t
*
3
3
)
(
s
m
Calculation of the average velocity:
3
2
1
3
2
1
t
t
t
s
s
s
t
s
v
total
total
s
m
After having discussed the basic principles one has the possibility of
creating
examples in a great variety.
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