What is Acceleration?
• Acceleration
– the change in an object’s velocity
over time.
• What are 2 ways that an object’s
velocity can change?
– change in speed
– change in direction
Change either one and
there is an acceleration
Average Acceleration
• To find the acceleration, we can
use the following equation:
average acceleration =
change in velocity
time to make the change
or
a=
∆v v − v 0
=
∆t t − t 0
units =
m
s =m
s
s2
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Graphing Acceleration:
Speed vs. Time Graphs
14
Speed (m/s)
12
10
8
6
4
2
0
0
1
2
3
4
5
6
Time (s)
1) Speed is increasing with time = accelerating
2) Line is straight = acceleration is constant
Graphing Acceleration:
Displacement vs. Time Graphs
35
Distance (m)
30
25
20
15
10
5
0
0
1
2
3
4
5
Time (s)
1) On Displacement vs. Time graphs a curved line
means the object is accelerating.
2) Curved line also means your speed is increasing.
Remember slope = speed.
Question
14
Speed (m/s)
12
10
Run = 3 s
8
6
Rise = -6 m/s
4
2
0
0
1
2
3
4
5
6
Time (s)
Above is a graph showing the speed of a car over time.
1) How is the speed of the car changing (speeding up,
Slowing down, or staying the same)?
2) What is this car’s acceleration?
1) The car is slowing down
2) Acceleration = rise/run = -6m/s ÷3s = -2 m/s2
2
Question:
35
Distance (m)
30
25
20
15
10
5
0
0
1
2
3
4
5
Time (s)
1) Which line represents an object that is accelerating?
The black and red lines represent a objects that are
accelerating. Black is going a greater distance each second, so it
must be speeding up. Red is going less each second, so must be
slowing down
Remember: in distance vs. time graphs:
curved line = accelerating, flat line = constant speed
Question: Hard one
Distance (m)
Speed (m/s)
14
45
40
12
35
10
30
258
206
15
4
10
52
00
0
0
11
22
33
4 4
5 5
6
6
Time
Time
(s)(s)
Above is a graph showing the speed of a car over time.
1)What would a velocity vs. time graph for this
look like?
Graphing Acceleration: Finding
Equations
• Velocity vs. Time
What is the slope
of this line?
vf
How would you
find the final
velocity of the
object?
vo
0
t
3
Graphing Acceleration :Finding
Equations
• Velocity vs. Time
How would you
find the final
position of the
object?
vf
vo
t
0
Constant Acceleration
Equations
• When acceleration is constant,
we can find other information
about the object’s motion using
the following equations:
v = v0 + at
1
x = x0 + v0t + at 2
2
2
2
v = v0 + 2a ( x − x0 )
Falling Objects
• Gravity acts on all falling (and
rising) objects.
• Down is considered to be in the
negative direction. Up is
positive.
• Acceleration due to gravity is
9.80 m/s2 downward (-9.80 m/s2)
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Helpful Hints
• List the variables that are given
and the one you are looking for
• Look for the words “from rest”
and “stop”
• Choose the equation with all
variables in it.
• Remember all direction
conventions
Sample Problem
• A cat accelerates from rest at a
constant rate of 2.30 m/s2 for 6.3
seconds.
What is the speed of the cat at
the end of the time?
How far does the cat travel in
this time?
Sample Problem
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Return to Honors
Physics Notes
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