Kinematics - Barransclass.com

doutfanaticalMechanics

Nov 14, 2013 (3 years and 10 months ago)

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Labs

and

discussions

have

already

started

Objectives


Relate distance, velocity, and acceleration.


Interpret distance
-
time, velocity
-
time, and
acceleration
-
time plots.

Describing Motion

It’s all math today

The Tortoise and the Hare

Told in words,
formulas, and
graphs

Poll Question

Who was faster?

A.
The
tortoise
.

B.
The
hare
.

C.
They had the
same
speed.

D.
What do you mean by faster?

Group Work: Graph

1.
Describe the Tortoise
-
and
-
hare race
using a
position
-
time graph.


Same axes


One world
-
line for tortoise, another for hare


Indicate significant times and positions

Speed

average

speed =

D
d

D
t

over
entire interval

instantaneous

speed = lim

D
d

D
t

at
one instant

D
t

0

Rate of changing position

Speed as Slope

Speed =

D

distance

D

time

distance

time

= slope of graph!

D

d

D

t

Poll Question

Who had the highest
average

speed
overall?

A.
The
tortoise
.

B.
The
hare
.

C.
Their average speeds were the
same
.

Poll Question

Who had the highest
instantaneous

speed?

A.
The
tortoise
.

B.
The
hare
.

C.
Their instantaneous

speeds were the
same
.

D.
At what time?

Example: Quantify

If we know definite distance and time values:

a.
What distance was the course?

b.
When did the hare stop?

c.
When did the hare wake?

d.
When did the tortoise finish?

We can calculate velocities.

Speed Units

distance

time

=

m/s

Group Work: Graph

2.
Describe the Tortoise
-
and
-
hare race
using a
velocity
-
time graph.

Distance Change as Area


What are the
areas

under the tortoise’s
and hare’s velocity
-
time plots?

speed

time

t
1

t
2

t
3

hare

tortoise

area

=
v
D
t



=
D
(
distance)

t
0

t
4

Group Work: Graph

3.
A car waits at a stop light for 5

seconds,
smoothly
accelerates

to 15

m/s over
5

seconds, and then continues at 15

m/s.
Describe the car’s motion using a
velocity
-
time

graph.

Acceleration

Rate of changing velocity

average

acceleration =

D
v

D
t

over the
entire interval

instantaneous

acceleration = lim

D
v

D
t

D
t

0

at
one instant

Acceleration Units

velocity

time

=

s

m/s

=
m/s
2

Group Work: Graph

4.
What is the car’s
acceleration

at the
different times? Describe the car’s
motion using an
acceleration
-
time graph.

Group Work: Compute

5.
How
far

does the car go:

a.
Between 0

s and 5

s?

b.
Between 10

s and 15

s?

Acceleration

Starting from a traffic light that turns green

d

t

v

t

a

t

area

=
velocity

area

=
distance

slope

=
velocity

slope

=
acceleration

Group Work 6

Describe four ways:

time

position

0

Group Work 6

Describe four ways:

time

velocity

0

Group Work 6

Describe four ways:

time

acceleration

0

Group Work 6

Describe four ways:

A coconut hangs motionless from its tree,
then drops with increasing downward speed
until it lands on the ground, quickly coming
to rest.

Formulas for Constant
Acceleration


Velocity change
D
v

=

a

D
t


Velocity
v
t

=
v
0

+
D
v

=
v
0

+
a

D
t


Position change
D
x

=
v
0
D
t
+ 1/2
a

(
D
t
)
2


Position
x
t

=
x
0

+
v
0
D
t
+ 1/2
a

(
D
t
)
2

Reading for Next Time


Vectors
: how we handle quantities with
directions


Important vectors:
position
,
velocity
,
acceleration
,
force