Kinematics: Combined Motion

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14 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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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.