Physics

L3

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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

Elapsed

Time (s)

Instantaneous Speed (m/s)

0 0

1 10

2 20

3 30

4 40

5 50

. .

. .

t 10t

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

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

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)

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

• 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

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]

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)

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

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

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

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?

€

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

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?

End L3

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