I would suggest you take notes like this:
You will need 4 page sides
(2 pages, front & back)
Leave page 1 blank and start on page #2.
(See next slide)
I would suggest you take notes like this:
VELOCITY EQUATIONS
(1)
I would suggest you take notes like this:
Starting from rest vi = 0
(2)
Already moving vi ≠ 0
(3)
7
5
4
3
1
2
Velocity (m/s)
6
vf
0
vi
0
1
2
3
4
5
6
7
Time (s)
Page 2
8
9
10
11
12
13
7
5
4
1
2
3
vavg
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
How would we calculate Vavg?
5
4
1
2
3
vavg
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
vavg = (vi + vf)/2
5
4
1
2
3
vavg
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
What about acceleration?
5
4
1
2
3
vavg
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
a = Δv/Δt
5
4
1
2
3
vavg
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
a = Δv/Δt
6
4
5
This is just the 'rise' divided by the 'run'. So the slope of velocity time graph gives us acceleration!
1
2
3
vavg
vi
0
Velocity (m/s)
}
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
a = Δv/Δt
a = (vf ­ vi)/t
5
4
1
2
3
vavg
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
a = Δv/Δt
a = (vf ­ vi)/t
5
4
IF:
vi = 3
vavg
1
2
Then:
a = vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
a = Δv/Δt
a = (vf ­ vi)/t
5
4
IF:
m
vi = 0 /s
3
vavg
1
2
Then:
a = vf/t
vf = at
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
If vi < or vi > 0:
3
4
5
(Which do we have here?)
2
Velocity (m/s)
6
7
vf
0
1
vi
0
1
2
3
4
5
6
7
8
9
10
11
Time (s)
(Page 3)
NEW GRAPH!!!!
12
13
7
vf
If vi < or vi > 0:
5
EXACTLY the same as our other graph!!!
2
3
4
vavg
1
vi
0
Velocity (m/s)
6
vavg = (vi + vf)/2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
If vi < or vi > 0:
a = Δv/Δt
5
a = (vf ­ vi)/t
2
3
4
vavg
1
vi
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
If vi < or vi > 0:
a = Δv/Δt
5
a = (vf ­ vi)/t
4
vavg
2
3
at = vf ­ vi
1
vi
vf = vi + at
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
Page 1
How to 'READ' the equations:
vf = vi + at
How fast I'm going now depends on: Was I moving to start out?
AND
Did I speed up or slow down, and if so, for how long?
How would we calculate the area of this triangle?
7
How would we calculate the area of this triangle?
5
4
3
vavg
1
2
Velocity (m/s)
6
vf
0
vi
0
1
2
3
4
5
6
7
Time (s)
Page 2
8
9
10
11
12
13
7
How would we calculate the area of this triangle?
4
5
Area=½ b*h
1
2
3
vavg
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
How would we calculate the area of this triangle?
5
Area=½ b*h
4
But instead we have:
3
vavg
1
2
Area=½ v*t
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
How would we calculate the area of this triangle?
5
Area=½ b*h
4
But instead we have:
3
vavg
2
Area=½ v*t
1
click here
DISPLACEMENT
vi
0
Velocity (m/s)
6
vf
0
1
2
3
4
5
6
7
8
9
10
11
12
Time (s)
WHAT DOES AREA TELL YOU IN THIS CASE?
(HINT: Think Units, Think STD Lab)
13
Page 1
Interpreting Graphs:
The slope of a Displacement vs. Time graph tells us ___________.
The slope of a Velocity vs. Time graph tells us ________________.
The area under a Velocity vs. Time graph tells us ______________.
Interpreting Graphs:
The slope of a Displacement vs. Time graph tells us ___________.
Velocity
The slope of a Velocity vs. Time graph tells us ________________.
Acceleration
The area under a Velocity vs. Time graph tells us ______________.
Displacement
5
4
3
vavg
1
2
Velocity (m/s)
6
7
Remember from before:
vf For vi=0:
a=vf/t
vf=at
0
vi
0
1
2
3
4
5
6
7
Time (s)
Page 2
8
9
10
11
12
13
5
4
Displacement = ½ v*t
1
2
3
vavg
vi
0
Velocity (m/s)
6
7
Remember from before:
vf For vi=0:
a=vf/t
vf=at
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
4
Displacement = ½ v*t
3
vavg
1
2
d = ½ (at)*t
vi
0
Velocity (m/s)
6
7
Remember from before:
vf For vi=0:
a=vf/t
vf=at
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
4
Displacement = ½ v*t
3
vavg
2
d = ½ (at)*t
1
d = ½ at2
vi
0
Velocity (m/s)
6
7
Remember from before:
vf For vi=0:
a=vf/t
vf=at
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
4
Displacement = ½ v*t
3
vavg
2
d = ½ (at)*t
1
d = ½ at2
vi
0
Velocity (m/s)
6
7
Remember from before:
vf For vi=0:
a=vf/t
vf=at
0
1
2
3
4
5
6
7
8
9
10
11
12
Time (s)
What does the 'slope' tell us again?
13
d = area under graph
5
3
4
vavg
2
Velocity (m/s)
6
7
vf
0
1
vi
0
1
2
3
4
5
6
7
Time (s)
Page 3
8
9
10
11
12
13
d = area under graph
5
top triangle:
2
3
4
vavg
1
vi
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
d = area under graph
5
top triangle:
d= ½ at2
2
3
4
vavg
1
vi
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
d = area under graph
5
top triangle:
d= ½ at2
bottom rectangle:
2
3
4
vavg
1
vi
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
d = area under graph
5
top triangle:
d= ½ at2
bottom rectangle:
d= vi * t
2
3
4
vavg
1
vi
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
d = area under graph
5
top triangle:
d= ½ at2
bottom rectangle:
d= vi * t
3
4
vavg
2
Total area:
1
vi
d= vit + ½at2
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
d = area under graph
5
top triangle:
d= ½ at2
bottom rectangle:
d= vi * t
3
4
vavg
2
Total area:
1
vi
d= vit + ½at2
0
Velocity (m/s)
6
7
vf
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Time (s)
... and what does the 'slope' tell us again?
Page 1
How to 'READ' the equations (cont.):
d = vit + ½at
2
Where I'm at now depends on: Was I moving to start out with, and if so, how much time has passed since then?
AND
Did I speed up or slow down
during this time?
Your notes should now look like this:
VELOCITY EQUATIONS
How to 'READ' the equations:
vf = vi + at
How fast I'm going now depends on: Was I moving to start out?
AND
Did I speed up or slow down, and if so, for how long?
d = vit + ½at2
Where I'm at now depends on: Was I moving to start out with, and if so, how much time has passed since then?
AND
Did I speed up or slow down during this time?
Interpreting Graphs:
Velocity
The slope of a Displacement vs. Time graph tells us _________.
Acceleration
The slope of a Velocity vs. Time graph tells us ______________.
The area under a Velocity vs. Time graph tells us ___________.
Displacement
(1)
Ah...beautiful, colorful, candy­like notes:
Starting from rest vi = 0
Already moving vi ≠ 0
vavg
Displacement
Displacement
vavg = (vi + vf)/2
a = Δv/Δt
a = (vf ­ vi)/t
IF:
vi = 0 m/s
d = ½ at2
vavg = (vi + vf)/2
If vi < or vi > 0:
a = Δv/Δt
a = (vf ­ vi)/t
at = vf ­ vi
Then:
a = vf/t
vf = at
d = area under graph
top triangle:
d= ½ at2
bottom rectangle:
d= vi * t
vf = vi + at
Total area:
d= vit + ½at2
(2)
(3)
HOW FAR EXAMPLE:
PAGE 4:
(4)
5
4
1
2
3
How far does this graph get us?
0
Velocity (m/s)
6
7
d= vit + ½at2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
4
3
2
1
0
Velocity (m/s)
6
7
d= vit + ½at2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
1
2
3
4
vf
vi
0
Velocity (m/s)
6
7
vit ½at2
d= + 0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
a = Δv/Δt
vf
1
2
3
4
a = vf ­ vi
tf ­ ti
vi
0
Velocity (m/s)
6
7
vit ½at2
d= + 0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
a = Δv/Δt
vf
3
4
a = vf ­ vi
tf ­ ti
2
a = (4 ­ 0)m/s
(4 ­ 0)s
1
m 2
a
= 1 /s
vi
0
Velocity (m/s)
6
7
vit ½at2
d= + 0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
vit ½at2
d= + 5
1
2
3
4
vf
vi
0
Velocity (m/s)
6
a = 1 m/s2
0
1
2
3
2
4
5
d = ½at
d= ½(1m/s2)(4s)2
d= 8m
6
7
Time (s)
8
9
10
11
12
13
5
2
3
4
vi
1
d = ½at2 d = 8m
0
Velocity (m/s)
6
7
d= vit + ½at2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
2
3
4
vi
1
d = ½at2 d = 8m
d = vi*t
d=4m/s*4s
d=16m
0
Velocity (m/s)
6
7
d= vit + ½at2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
vf
5
2
3
4
vi
1
d = ½at2 d = 8m
d = vi*t
d=4m/s*4s
d=16m
0
Velocity (m/s)
6
7
d= vit + ½at2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
vf
5
4
vi
2
3
d= vit + ½at2
1
d = ½at2 d = 8m
d = vi*t
d=4m/s*4s
d=16m
0
Velocity (m/s)
6
7
d= vit + ½at2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
vf
6
7
d= vit + ½at2
5
vi
4
a = vf ­ vi
tf ­ ti
2
3
d= vit + ½at2
1
d = ½at2 d = 8m
d = vi*t
d=4m/s*4s
d=16m
0
Velocity (m/s)
a = Δv/Δt
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
vf
6
7
d= vit + ½at2
5
vi
4
a = vf ­ vi
tf ­ ti
2
3
d= vit + ½at2
1
d = ½at2 d = 8m
d = vi*t
d=4m/s*4s
d=16m
a = (6 ­ 4)m/s
(12 ­ 8)s
a = 0.5 m/s2
0
Velocity (m/s)
a = Δv/Δt
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
7
d= vit + ½at2
m
5
vf
4
vi
2
3
d= vit + ½at2
d = 4m/s*4s+½(0.5m/s2)(4s)2
d = 20m
1
d = ½at2 d = 8m
d = vi*t
d=4m/s*4s
d=16m
0
Velocity (m/s)
6
a = 0.5 /s
2
0
1
2
3
4
5
6
7
Time (s)
8
9
10
11
12
13
5
4
2
3
d= vit + ½at2
d = 4m/s*4s+½(0.5m/s2)(4s)2
d = 20m
1
d = ½at2 d = 8m
d = vi*t
d=4m/s*4s
d=16m
0
Velocity (m/s)
6
7
d= vit + ½at2
0
1
2
3
4
5
6
7
8
9
10
11
12
Time (s)
dtotal = 8m + 16m + 20m = 44m
13
HOW FAR EXAMPLE:
d=16m
d = 20m
d= 8m
PAGE 4:
a = Δv/Δt
a = vf ­ vi
tf ­ ti
d = vi*t
d=4m/s*4s
d=16m
a = Δv/Δt
a = vf ­ vi
tf ­ ti
a = (4 ­ 0)m/s
(4 ­ 0)s
a = (6 ­ 4)m/s
(12 ­ 8)s
a = 1 m/s2
a = 0.5 m/s2
d= vit + ½at2
d = 4m/s*4s+½(0.5m/s2)(4s)2
d = 20m
d = ½at2
d= ½(1m/s2)(4s)2
d= 8m
dtotal = 8m + 16m + 20m = 44m
(4)
Page 5
(Hey wait a minute, you said there were only 4 pages of notes?!?!)
Formulas
Variables Solved/Known
d
vavg = Δd/Δt
vi
vf
*
*
*
vavg = (vi + vf)/2
*
*
vf=vi+at
*
*
*
a
*
a = Δv/Δt
d= vit + ½at2
vavg
*
t
*
*
*
*
*
*
*
*
THIS CAN BE PRINTED OUT FROM THE PHYSICS WEBPAGE!!!
I would suggest you take notes like this:
If you are
going to
transfer the
equation
sheet into
your notes,
give them
their own
page.
They're that
IMPORTANT!!!
(5)