Topic 1.3
Topic 1.3. constant velocity uniform motion changing velocity accelerated motion.
Jan 02, 2016
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Topic 1.3
•constant velocity•uniform motion
•changing velocity•accelerated motion
t
dv
t
dvav
Any change in velocity …
• Speeding up
• Slowing down
• Changing direction
We define acceleration as …
calculatest
v
… the exact acceleration when the acceleration is uniform
… the average acceleration when it isn’t
Since we are using the same formula regardless of whether or not the acceleration is uniform we are not going to make a big deal of differentiating between the exact and average acceleration.
Sample Problem
• A car accelerates at a constant rate from 40 km/h[E] to 90 km/h[E] in 5.0s. What is its acceleration?
Every second the velocity increases by 10 km/h towards the East
[E] is +ive
Sample Problem
• A car accelerates at a constant rate from 40 km/h[E] to 90 km/h[E] in 5.0s. What is its acceleration?
Every second the velocity increases by 2.8 m/s towards the East
[E] is +ive
Sample Problem
• A runner starting from rest reaches a velocity of 9.6 m/s in 2.0s. What is her average acceleration?
Assume she runs in the +ive direction
Every second the velocity increases by 4.8 m/s
Sample Problem
• A baseball player running at 8.0m/s[W] slides into third base, coming to rest in 1.6s. What is his average acceleration?
[w] is +ive
Slowing down as you go west is the same as speeding up towards the east
Practice
• Topic 1.3 Acceleration (Handout #1)
Assignment
the slope of the line on a d-t graph
Recall, straight line on a d-t graph means …
… UniformMotion or ConstantVelocity
Graphing Motion+
Time (s) Velocity (m/s)
0 0
5 +4
10 +8
15 +12
20 +16
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t (s)
V (
m/s
)Straight line on a v-t graph means…
…Uniform or constant acceleration
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
t (s)
V (
m/s
)
grapht vaon line theof slope12
12
tt
vv
t
va
Sample ProblemDetermine the object’s acceleration for …
0
10
20
30
40
50
60
0 2 4 6 8 10 12 14 16 18 20
t (s)
V (
m/s
)
a) the first 8s
0
10
20
30
40
50
60
0 2 4 6 8 10 12 14 16 18 20
t (s)
V (
m/s
)
b) from 8s to 12s
0
10
20
30
40
50
60
0 2 4 6 8 10 12 14 16 18 20
t (s)
V (
m/s
)
Sample Problem
0
5
10
15
20
25
0 5 10 15 20 25 30
t (s)
V (
m/s
) A
B
C
Determine the acceleration for each lettered section.
A
B
C
A:
0
5
10
15
20
25
0 5 10 15 20 25 30
t (s)
V (
m/s
)
A
B
C
B:
2m/s0a
0
5
10
15
20
25
0 5 10 15 20 25 30
t (s)
V (
m/s
)
A
B
C
C:
0
5
10
15
20
25
0 5 10 15 20 25 30
t (s)
V (
m/s
)
Practice
• Topic 1.3 Acceleration (Handout #2)
Assignment 2
Sample Problem• The graph shows the motion of a car for a 10s
interval. What is the displacement of the car during this time interval?
Consider the rectangle formed by the graph line and time axis
Length = 10s
Width = 20m/s
The displacement in any time interval is given by the area under the v-t graph
Check out
• http://www.surendranath.org/Applets/Math/IntArea/IA.html
• http://www.physics101online.com/physics101/mechanics/motion-in-1d/area-under-v-vs-t-curve-text
The graph shows the velocity of a ball that starts from rest and rolls down a long hill. What is the ball’s displacement after 10s?
Base=10s
Height=20m/s
The graph shows the motion of a dog running up and down a straight road for a 16s interval. What is the dogs displacement over that time interval?
Practice
• Topic 1.3 Acceleration (Handout #3)
Assignment 3
Uniform Motion
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Bodies in Free Fall
• Free fall refers to any body falling under the influence of gravity alone
• That is, the only force that acts on a freely falling object is gravity
How do things fall?
• Aristotle (384 - 322 BC) said that objects would fall at a constant speed and that the speed of a falling object would be proportional to its mass
• That is, a 2kg stone would fall twice as fast as a 1kg stone
• This went unchallenged for nearly 2000 years
• Galileo (1564 – 1642) hypothesized that objects do not fall at a constant speed, but accelerate
• He conducted experiments using balls rolled down inclined planes and a water clock
• He concluded that objects in free fall undergo uniform acceleration
• He also concluded that in the absence of air resistance the acceleration of a freely falling body is independent of mass
• Near the surface of the earth the acceleration due to gravity, denoted g, is …
• g = 9.8m/s2
• It varies slightly from location to location due to:– elevation– latitude– topography– geology
• Since freely falling bodies experience uniform acceleration, the equations we derived earlier also apply when solving free fall problems
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