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Acceleration
∆ v�t
a =
Change in Velocity�Time
≡
m�s�s
a = 5
m�s·s
a = 5
m�s2
a = 5
Example:
1
m�s
1�s
m�s2
Acceleration = 5
EVERY second the velocity changes by 5 m/s
Vf = a·t
35
7
30
6
25
5
20
4
15
3
10
2
5
1
0
0
Instantaneous�Velocity (m/s)
Time�(seconds)
Vf = 5·0 = 0
Vf = 5·1 = 5
Vf = 5·2 = 10
Vf = 5·3 = 15
Vf = 5·4 = 20
Vf = 5·5 = 25
Vf = 5·6 = 30
Vf = 5·7 = 35
What is the instantaneous velocity after 30 seconds?
Vf = 5·30 = 150
0
10
20
30
40
50
60
70
80
90
100
110
120
130
meters per second
0
10
20
30
40
50
60
70
80
90
100
110
120
130
meters per second
Acceleration = 13 m/s2
Acceleration = 3 m/s2
?
?
Time = seconds
0
1
2
3
4
5
6
7
8
10
9
0
1
2
3
4
5
6
7
8
10
9
Free Fall
I can . . .
�
Does a ball dropped�from your hand�ACCELERATE?
Does it accelerate�UNIFORMLY?
1 ft
2 ft
3 ft
4 ft
5 ft
Acceleration = 1 ft/s2
10 cm
20 cm
30 cm
40 cm
50 cm
10 cm
20 cm
30 cm
40 cm
50 cm
Clifton Bluhm
10 cm
20 cm
30 cm
40 cm
Clifton Bluhm
Clifton Bluhm
A ball dropped from�your hand DOES�accelerate UNIFORMLY.
Do ALL things�uniformly accelerate at the�SAME RATE?
http://upload.wikimedia.org/wikipedia/commons/f/f2/Leaning_Tower_of_Pisa.jpg
Construction began in 1178�and was finished about 200 years later.
Galileo Galilei�(1564 – 1642)
Book
Paper
Feather
Penny
http://www.lakewoodconferences.com/direct/dbimage/50269602/Artificial_Feather.jpg
http://www.enasco.com/prod/images/products/56/NC29918Cl.jpg
Video Courtesy of NASA
Commander David Scott - Apollo 15
Video Courtesy of NASA
Commander David Scott - Apollo 15
ALL things DO�accelerate�at the same rate.
At WHAT RATE do�they accelerate?
Acceleration of Gravity = -9.79604 ± .00002 m/s2
All freely falling objects�(in the absence of air resistance)�accelerate at the same rate.
g = -9.80 m/s2
g = -32.2 ft/s2
agravity = -9.80 m/s2
Time�(seconds) | Instantaneous�Velocity (m/s) |
0 | 0 |
1 | 10 |
2 | 20 |
3 | 30 |
4 | 40 |
5 | 50 |
6 | 60 |
7 | 70 |
g = -9.80 m/s2 ≈ -10 m/s2
If this space ship accelerates at 9.80 m/s2, �how long would it take to reach Warp 1? �(2.998 x 108 m/s or 299,800,000 m/s)
vf = a∙t
299,800,000 = 9.80∙t
http://www.desktopwallpaperhd.com/wallpapers/32/55158.jpg
t = 30,600,000 s
t = 354 days
http://static.howstuffworks.com/gif/speedometer-1.jpg
0
10
20
30
40
50
60
70
80
90
100
110
120
130
meters per second
The velocity of an object in freefall changes by approximately�10 m/s each second.
An object in freefall accelerates at approximately�10 m/s2
0
10
20
30
40
50
60
70
80
90
100
110
120
130
meters per second
BBC Video, “Planet Earth”
Discovery SCIENCE
990 km/hr = 620 mi/hr
Transporter 2
0
10
20
30
40
50
60
70
80
90
100
110
120
130
0
10
20
30
40
50
60
70
80
90
100
110
120
130
0
10
20
30
40
50
60
70
80
90
100
110
120
130
0
1
2
3
4
Time = seconds
V0 = 20 m/s
Hang Time
http://upload.wikimedia.org/wikipedia/commons/d/d3/Spiegel_Building_Hamburg_3.jpg
0
10
20
30
40
50
60
70
80
90
100
110
120
130
Time = seconds
0
1
2
3
4
5
6
7
8
10
9
V0 = 50 m/s
Hang Time
http://upload.wikimedia.org/wikipedia/commons/d/d3/Spiegel_Building_Hamburg_3.jpg
0
10
20
30
40
50
60
70
80
90
100
110
120
130
Time = seconds
0
1
2
3
4
5
6
7
8
10
9
V0 = 50 m/s
http://upload.wikimedia.org/wikipedia/commons/d/d3/Spiegel_Building_Hamburg_3.jpg
50 40 30 20 10 0 -10 -20 -30 -40 -50
(m/s)
Time = seconds
0
1
2
3
4
5
6
7
8
10
9
http://upload.wikimedia.org/wikipedia/commons/d/d3/Spiegel_Building_Hamburg_3.jpg
50 40 30 20 10 0 -10 -20 -30 -40 -50
(m/s)
1 s
10 m/s
Acceleration = -10 m/s2
Velocity = 0 m/s
0
10
20
30
40
50
60
70
80
90
100
110
120
130
Time = seconds
0
1
2
3
4
5
6
V0 = 20 m/s
Hang Time
http://upload.wikimedia.org/wikipedia/commons/d/d3/Spiegel_Building_Hamburg_3.jpg
0
10
20
30
40
50
60
70
80
90
100
110
120
130
Time = seconds
0
1
2
http://upload.wikimedia.org/wikipedia/commons/d/d3/Spiegel_Building_Hamburg_3.jpg
V0 = 20 m/s
-20 m/s
I can . . .