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Physics
L3
www.slideshare.net/DMS_physics
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Free Fall
• … occurs if the only force on an object is gravity.
• Acceleration of gravity
€
g = 9.81 m /s2
For convenience we can use g = 10 m/s2
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Elapsed
Time (s)
Instantaneous Speed (m/s)
0 0
1 10
2 20
3 30
4 40
5 50
. .
. .
t 10t
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How Fast ?
€
g ≈10 m /s2
(acceleration of gravity)€
a = g =change in( )v
t
g =v − v0
t=
v − 0
t
g =v
t
€
v = gt
€
rv
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Question
• What would the speed of the apple be
– after 4.5s?– after 8s?– after 15s?
Elapsed
Time (s)
Instantaneous
Speed (m/s)0 0
1 10
2 20
3 30
4 40
5 50
. .
. .
t 10t
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Speed Graph
• In Uniform Motion
– speed is directly proportional to time
– The graph is a straight line
– The slope is acceleration
Speed vs. Time
0
10
20
30
40
50
60
0 2 4 6
time (s)
speed (m/s)
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Question
• What would the speed of the apple be
– after 4.5s?– after 8s?– after 15s?
• 45 m/s• 80 m/s• 150 m/s
€
v = 10 m /s2( )t
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• Acceleration is 10m/s2
downwards at all times
• At the same height– Speeds are the same– Velocities are in the
opposite directions
t = 3s, v = 0m/s
t = 2s
t = 1s
t = 0s
t = 4s
t = 5s
t= 6s
t = 7s
v = 20m/s
v = 10m/s
v = 30m/s
v = 40m/s
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t = 3s, v = 0m/s
t = 2s
t = 1s
t = 0s
t = 4s
t = 5s
t= 6s
t = 7s
v = 20m/s
v = 10m/s
v = 30m/s
v = 40m/s
Velocity vs. Time
-50
-40
-30
-20
-10
0
10
20
30
40
0 5 10
time (s)
velocity (m/s) [up]
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t = 3s, v = 0m/s
t = 2s
t = 1s
t = 0s
t = 4s
t = 5s
t= 6s
t = 7s
v = 20m/s
v = 10m/s
v = 30m/s
v = 40m/s
Speed vs. Time
05
1015202530354045
0 5 10
time (s)
speed (m/s)
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Average Speed• For objects moving with
constant acceleration, the average speed is the arithmetic mean (average) of the initial and final speeds.
Elapsed
Time (s)
Instantaneous
Speed (m/s)0 0
1 10
2 20
3 30
4 40
5 50
. .
. .
t 10t €
v =v1 + v2
2
€
v =10 m /s( ) + 20 m /s( )
2=15 m /s
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How far ?
€
d = v t
d =v0 + v
2
⎛
⎝ ⎜
⎞
⎠ ⎟t =
0 + v
2
⎛
⎝ ⎜
⎞
⎠ ⎟=
1
2v
d =1
2v ⋅ t but v = gt
d =1
2gt( )t
€
d =1
2gt 2
€
d
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How far ?
€
d =1
2gt 2
Elapsed
Time (s) Distance (m)
0 0
1 5
2 20
3 45
4 80
5 125
. .
. .
t 5t2
€
d = 5 m /s2( )t
2
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Classwork (p.20/Q)
• An apple falls from a tree and hits the ground in one second.
– What is its speed upon striking the ground?– What is its average speed during this 1s?– How high above the ground was the apple
when it was dropped?
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€
t =1s
_________________
a) v = ?
b) v = ?
c) d = ?
a)
v = gt = 10m /s2( ) 1s( ) =10m /s
b)
v =v0 + v
2=
0 + 10m /s( )2
= 5m /s
c)
d =1
2gt 2 =
1
210m /s2( ) 1s( )
2= 5m
or
d = v t = 5m /s( ) 1s( ) = 5m
€
d
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Homework Assignment
• P.26 / 16,17,19– For a freely falling object dropped from
rest, what is the• Instantaneous speed at the end of the fifth
second of fall?• Acceleration at the end of the fifth second of
fall?• Distance covered by the end of the fifth second
of fall?
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End L3
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