Kinematics PPT - Jpsaos.com

doutfanaticalMechanics

Nov 14, 2013 (3 years and 9 months ago)

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Kinematics

The study of how objects move

Where are You?

We must start with a
question

Position

Reference Point:

Zero location in a coordinate
system or frame.

Frame of Reference:

Coordinate system used to define
motion.

Position:

Separation between an object and a
reference point. It needs a distance and direction.


i.e. 3.0 meters to the right.

To find where you are you need the following:

You are Here

You are Here

You are Here

You are Here

You are Here

You are Here

You are Here

You are Here

Distance vs. Displacement

Distance is simply the total path length
traversed in moving from one location
to another

Distance is a SCALAR quantity. A measurement
with only magnitude, or size.

50 m

Distance vs. Displacement

Displacement is the straight
-
line distance between
two points, along with the direction from the
starting point to the final position.

Displacement is a VECTOR quantity. A
measurement with magnitude, or size and
a direction

10 m East

Difference between
Distance and
Displacement

Walking to
Physics Lab

Distance = 8 m

Displacement = 8m right

Right
-

Positive

Left
-

Negative

Direction Convention :

Displacement =+8m

Speed

Speed
Time

Distance
Speed is the rate at which distance is traveled.

=10 m/s

20 m

2 sec

Speed
m

20
2
sec
Speed is a scalar
quanity

Average speed

is the distance
d

traveled, the actual path, divided
by the total time
t

elapsed in traveling that distance.

Average Sp
eed
Distance T
raveled
Total Time

Instantaneous Speed

is how fast an object is moving at a
particular instant of time.

Average vs.
Instantaneous Speed

Velocity

V
x
t
x
x
t
t
o
o






x
o
t
o
Velocity

tells how fast something is moving
and

in what
direction. Velocity is a vector quantity.

Average Velocity

is the displacement divided by the total
travel time

=initial position, commonly
zero

= initial time, commonly zero

V
x
t

When x
o

and t
o

are zero

A jogger jogs from one end to the other of a straight 300 meter track
(from point A to point B) in 2.50 min and then turns around and
jogs 100 m back toward the starting point (to point C) in another
1.00 min. What are the jogger’s average speeds and velocities in
going

A)

From A to B

B) From A to C after turning around

Speed
and
Velocity
Problem

avg speed



d
t
m
s
m
s
300
150
2
00
.
v
x
t
m
s
B
B
m
s





300
150
2
00
.
A)

v
x
x
t
t
m
m
s
s
c
B
C
B
C
m
s










300
100
150
60
0
0
952
(
)
.
.
Given:

x
B

= 300m
-

0m = +300m (from A to B)

x
C

= 200m


300m =
-
100m (from B to C)

t
B

= 2.50 min = 150 s

t
C

= 1.00 min = 60.0 s


B)

Average speed and velocity from A to B

Average speed and velocity from A to C

avg speed





d
t
m
m
s
s
m
s
300
100
150
60
0
1
90
.
.
Two Components
of Velocity

Graphical look
at Motion

Acceleration

Position is the separation between an object
and a reference point.

Displacement is a change in position

Velocity is the time rate change of displacement

Acceleration is the time rate change of velocity

All four are vector quantities

Represented by a magnitude and direction

K
i
n
e
m
a
t
i
c


E
q
u
a
t
i
o
n
s

v
d
t






d
d
t
t
2
1
2
1


d
d
t
2
1
a
v
t






v
v
t
t
2
1
2
1


v
v
t
2
1
v
v
at
2
1


acceleration

velocity

v
d
t

v
v
v


1
2
2
d
t


v
v
1
2
2
With a constant acceleration

Total Displacement and total time

Average Velocity

d
v
v
t


1
2
1
2
(
)
d
v
v
t


1
2
1
2
(
)
v
v
at
2
1


v
at
1

d
v
v
at
t



1
2
1
1
(
(
))
d
v
t
at


1
2
1
1
2
2
2
(
)
d
v
t
at


1
1
2
2
d
v
v
t


1
2
1
2
(
)
v
v
ad
2
2
1
2
2


d
v
v
a


2
2
1
2
2
d
v
v
v
v
a




1
2
2
1
2
t
v
v
a


2
1
d
v
t

v
v
at
2
1




v
v
1
2
2
v
v
v


1
2
2
v
v
a
2
1

K
i
n
e
m
a
t
i
c


E
q
u
a
t
i
o
n
s

v
d
t



v
v
at
2
1


a
v
t



d
v
t
at


1
1
2
2
v
v
ad
2
2
1
2
2


Problem:

Ally the Alligator takes off from an airfield.
She starts from rest and obtains a velocity of
36 m/s at take off in 20.0 seconds.

What is her acceleration down the runway?

How far did she go down the runway?

a
v
t





v
v
t
2
1


36
0
20
m
s
m
s
sec

1
8
2
.
m
s
1
8
2
.
m
s
d
v
v
t


1
2
1
2
(
)
d
m
s
m
s


1
2
0
36
20
0
(
)
.
sec
d
m

360