Describes displacement, velocity, acceleration as vectors and distance and speed as scalars, Show all needed equations and their use. **More good stuff available at: www.wsautter.com and http://www.youtube.com/results?search_query=wnsautter&aq=f

1. Copyright Sautter 2003

2. Measuring Motion
• The study kinematics requires the measurement of
three properties of motion.
• (1) displacement – the straight line distance between
two points (a vector quantity)
• (2) velocity – the change in displacement with respect
to time (a vector quantity)
• (3) acceleration – the change in velocity with respect to
time (a vector quantity)
• The term distance like displacement, refers to the
change in position between two points, but not in a
straight line. Distance is a scalar quantity. Speed refers
to change in position with respect to time but unlike
velocity, does not require straight line motion. Speed is
a scalar quantity.

3. Lake Tranquility
A x
x B
Distance traveled
from A to B
Displacement
from A to B
Speed = Distance from A to B/ time
Velocity = Displacement from A to B/ time

4. VELOCITY & ACCELERATION
• OBJECTS IN MOTION MAY MOVE AT CONSTANT
VELOCITY (COVERING EQUAL DISPLACEMENTS IN
EQUAL TIMES) OR BE ACCELERATED (COVER
INCREASING OR DECREASING DISPLACEMENTS IN
EQUAL TIMES).
• VELOCITY MEASUREMENTS MAY BE OF TWO TYPES,
AVERAGE VELOCITY (VELOCITY OVER A LARGE
INTERVAL TIME) OR INSTANTANEOUS VELOCITY
(VELOCITY OVER A VERY SHORT INTERVAL OF
TIME).
• ACCELERATION MAY BE UNIFORM OR NON
UNIFORM. UNIFORM OR CONSTANT ACCELERATION
REQUIRES THAT THE VELOCITY INCREASE OR
DECREASE AT A CONSTANT RATE WHILE NON
UNIFORM ACCELERATION DISPLAYS NO REGULAR
PATTERN OF CHANGE.

5. 1 sec 2 sec 3sec 4sec 5 sec
EQUAL DISPLACEMENTS IN EQUAL TIMES
1 sec 2 sec 3sec 4sec
REGULARLY INCREASING DISPLACEMENTS IN EQUAL TIMES
CLICK
HERE

6. S
D
I
S
P
L
A
C
E
M
E
N
T
time
t
S
t
S
t
POSITIVE
ACCELERATION
Equal time
intervals result
in increasingly
larger displacements

7. Average velocity
between t1 and t2
Is the slope of the
Secant line = S/ t
D
I
S
P
L
A
C
E
M
E
N
T
time
S
t
t1 t2
s1
s2
Secant
line

8. D
I
S
P
L
A
C
E
M
E
N
T
time
s1
t1
Finding velocity
at point t1, s1
(instantaneous velocity)
Draw a tangent line at the point
t
S
Find the slope of
the tangent line
Instantaneous velocity
equals the slope of
the tangent line

9. DISPLACEMENT, VELOCITY &
CONSTANT ACCELERATION
• The velocity of an object at an instant can be found by
determining the slope of a tangent line drawn at a point to
a graph of displacement versus time for the object.
• If several instantaneous velocities are found and plotted
against time the graph of velocity versus time is a straight
line if the object is experiencing constant acceleration.
• The slope of the straight line velocity versus time graph is
constant and since acceleration can be determined by the
slope of a velocity – time graph, the acceleration is
constant.
• The graph acceleration versus time for a constant
acceleration system is a horizontal line. (A slope of zero
since constant acceleration means that acceleration is not
changing with time!)

10. D
I
S
P
L
A
C
E
M
E
N
T
Time
V
E
L
O
C
I
T
Y
Time
A
C
C
E
L
E
R
A
T
I
O
N Time
S
t
t
v
Slope of a tangent drawn to a point on
a displacement vs time graph gives
the instantaneous velocity at that point
Slope of a tangent drawn to a point on
a velocity vs time graph gives the
instantaneous acceleration at that point
PLOT OF INSTANTANEOUS
VELOCITIES VS TIME

11. MEASURING VELOCITY & ACCELERATION
• VELOCITY IS MEASURED AS DISPLACEMENT PER
TIME. UNIT FOR THE MEASUREMENT OF VELOCITY
DEPEND ON THE SYSTEM USED. IN THE MKS SYSTEM
(METERS, KILOGRAMS, SECONDS) IT IS DESCRIBED IN
METERS PER SECOND.
• IN THE CGS SYSTEM (CENTIMETERS, GRAMS,
SECONDS - ALSO METRIC) IT IS MEASURED IN
CENTIMETERS PER SECOND.
• IN THE ENGLISH SYSTEM IT IS MEASURED AS FEET
PER SECOND.
• ACCELERATION IN THE MKS SYSTEM IS EXPRESSED
AS METERS PER SECOND PER SECOND OR METERS
PER SECOND SQUARED.
• IN CGS UNITS IT IS CENTIMETERS PER SECOND PER
SECOND OR CENTIMETERS PER SECOND SQUARED. IN
THE ENGLISH SYSTEM FEET PER SECOND PER SECOND
OR FEET PER SECOND SQUARED ARE USED.

12. GRAVITY & CONSTANT ACCELERATION
• Gravity is the most common constant acceleration
system on earth. As object fall under the influence of
gravity (free fall) they continually increase in velocity
until a terminal velocity is reached.
• Terminal velocity refers to the limiting velocity
caused by air resistance. In an airless environment the
acceleration provided by gravity would allow a
falling object to increase in velocity without limit
until the object landed.
• In most problems in basic physics air resistance is
ignored. In actuality, terminal velocity is related to air
density, surface area, the velocity of the object and
the aerodynamics of the object (the drag coefficient).

13. CLICK
HERE

14. 19.6 m
44.1 m
78.4 m
19.6 m/s
2.0 sec
29.4 m/s
3.0 sec
39.2 m/s
4.0 sec

15. CALCULATING AVERAGE VELOCITY
• Average velocity for an object moving with uniform
(constant) acceleration can be calculated in two ways.
• (1) average velocity = the change in displacement
(displacement traveled, s) divided by the change in
time ( t). (s is the symbol used for displacement)
• (2) average velocity = the sum of two velocities divided
by two (an arithematic average).


 

16. 16
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