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Chapter 2 Section 2:
Acceleration
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Motion Review
Speed is the rate that an object’s distance changes Distance is how far an object has travelled
Speed = distance/time
Velocity is rate that an object’s displacement changes Displacement is how far the object is from the starting point
Velocity = displacement/time
When an object travels in only one direction, it’s distance and displacement are the same! This means that the value of speed and velocity would also be the same. From this point on, we will assume that objects are moving in one
direction away from a starting point and therefore we will refer to velocity as a “speed” with a direction to stay consistent with your book.
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Speed vs. Time Graphs
What would a speed vs. time graph look like for:
An object with a constant speed?
An object speeding up?
An object slowing down?
Spee
d (
m/s
)
Time (s)
What is the object’s
speed at this point?
0 m/s
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Acceleration
Acceleration is the rate of change of velocity
When the velocity of an object changes, we call that
acceleration
Because we are calling velocity a “speed” with direction,
acceleration occurs when there is a change in how fast an
object is moving (speeding up or slowing down), the direction
in which it is moving, or both
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Positive Acceleration
Positive acceleration occurs when an object is
speeding up
Acceleration is in the same direction as the velocity
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Negative Acceleration
Negative acceleration occurs when an object is
slowing down
Acceleration is in the opposite direction of velocity
We do not call negative acceleration deceleration!
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Changing Direction
Any time an object changes direction, it’s velocity
changes even if it is travelling at a constant speed
This also means that acceleration changes when an object
changes direction even if it is travelling at a constant speed
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Graphing Acceleration
Because acceleration is a change in velocity over
time, we can use speed vs. time graphs to
determine if acceleration is positive or negative or if
there is no acceleration happening
Based on what you know about acceleration,
which graph(s) illustrate positive and negative
acceleration?
Sp
eed
(m
/s)
Time (s)
Sp
eed
(m
/s)
Time (s) S
pee
d (
m/s
) Time (s)
Negative
Acceleration
No
Acceleration
Positive
Acceleration
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Calculating Acceleration
Acceleration is a change in velocity over time.
acceleration (m/s2) = ∆𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 (
𝑚
𝑠)
𝑡𝑖𝑚𝑒 (𝑠)
or
acceleration (a) = 𝐹𝑖𝑛𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣𝑓 −𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣𝑖
𝑡𝑖𝑚𝑒 (𝑡)
or
a = 𝑣𝑓 − 𝑣𝑖
𝑡
𝒗𝒇 − 𝒗𝒊
t a
or m/s/s
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Acceleration Practice
1. If a race car goes from 0 to 50 m/s in 5 seconds, what is its acceleration?
a = 𝑣𝑓 − 𝑣𝑖
𝑡
a = 50
𝑚
𝑠 −0
𝑚
𝑠
5 𝑠
a = 50
𝑚
𝑠
5 𝑠
a = 10 m/s2
vi = 0 m/s vf = 50 m/s t = 5 s a = ?
For each problem:
List the givens
List the formula you will use
Write the givens in your formula, including units
Show all math calculations
List appropriate units on your final answer
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More Acceleration Practice
2. If a car travels at 26 m/s and hits the brakes for 4
seconds to come to a complete stop, what is its
acceleration?
For each problem:
List the givens
List the formula you will use
Write the givens in your formula, including units
Show all math calculations
List appropriate units on your final answer
vi = 100 m/s vf = 0 m/s t = 2 s a = ?
a = 𝑣
𝑓 − 𝑣𝑖
𝑡
a = 0
𝑚
𝑠 −26
𝑚
𝑠
4 𝑠
a = −26
𝑚
𝑠
4 𝑠
a = - 6.5 m/s 2
![Page 12: Chapter 2 Section 2: Acceleration - Chippewa Falls Middle …cfsd.chipfalls.k12.wi.us/faculty/dufnerre/cms_files/event... · · 2013-04-16Chapter 2 Section 2: Acceleration . Motion](https://reader033.vdocument.in/reader033/viewer/2022051407/5afb70367f8b9a44659050a0/html5/thumbnails/12.jpg)
More Acceleration Practice
3. If a person can accelerate from rest at 2 m/s2, how fast will he be running after 2 seconds?
For each problem:
List the givens
List the formula you will use
Write the givens in your formula, including units
Show all math calculations
List appropriate units on your final answer
vi = 0 m/s vf = ? t = 5 s a = 2 m/s2
𝑣𝑓 − 𝑣𝑖 = a x t
𝑣𝑓 − 0 𝑚/𝑠 = 2 m/s2 x 2 s
𝒗𝒇= 4 m/s
![Page 13: Chapter 2 Section 2: Acceleration - Chippewa Falls Middle …cfsd.chipfalls.k12.wi.us/faculty/dufnerre/cms_files/event... · · 2013-04-16Chapter 2 Section 2: Acceleration . Motion](https://reader033.vdocument.in/reader033/viewer/2022051407/5afb70367f8b9a44659050a0/html5/thumbnails/13.jpg)
More Acceleration Practice
4. How long would it take a race car to go from 0 m/s to 45 m/s if it can accelerate at 6 m/s2?
For each problem:
List the givens
List the formula you will use
Write the givens in your formula, including units
Show all math calculations
List appropriate units on your final answer
vi = 0 m/s vf = 45 m/s t = ? a = 6 m/s2
t = 𝑣
𝑓 − 𝑣𝑖
𝑎
t = 45
𝑚
𝑠 −0
𝑚
𝑠
6 𝑚/𝑠2
t = 45
𝑚
𝑠
6 𝑚/𝑠2
t = 7.5 s
![Page 14: Chapter 2 Section 2: Acceleration - Chippewa Falls Middle …cfsd.chipfalls.k12.wi.us/faculty/dufnerre/cms_files/event... · · 2013-04-16Chapter 2 Section 2: Acceleration . Motion](https://reader033.vdocument.in/reader033/viewer/2022051407/5afb70367f8b9a44659050a0/html5/thumbnails/14.jpg)
More Acceleration Practice
5. If a skier is going downhill with an acceleration of 3 m/s2 and has a velocity of 18 m/s after 3 seconds, what was her initial velocity?
For each problem:
List the givens
List the formula you will use
Write the givens in your formula, including units
Show all math calculations
List appropriate units on your final answer
vi = ? vf = 18 m/s t = 3 s a = 3 m/s2
𝑣𝑓 − 𝑣𝑖 = a x t
18 𝑚/𝑠 − 𝑣𝑖= 3 m/s 2 x 3 s
𝒗𝒊= 9 m/s 18 𝑚/𝑠 − 𝑣𝑖= 9 m/s
−𝑣𝑖= - 9 m/s