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Accelerated motion
Sultan, Ahmed, and Majed
are three runners
Majed is moving with decreasing speed
Sultan is moving with constant speed
Ahmed with increasing speed
Which dot diagram represents each one's movement?
Which runner's speed is changing?
\[.................................\]An object moving with non-constant speed has acceleration
Click here to show solution
In a running race, consecutive pictures were taken every second
of runner 7 who was moving with constant acceleration
To calculate acceleration
First find the change in velocity vector
\[\vec {∆𝜗}=\vec {𝑣_𝑓}−\vec {𝑣_𝑖}\]
Then calculate the time rate
of velocity change
\[\vec a=\frac{\vec {𝑣_𝑓}−\vec {𝑣_𝑖}}{∆t}\]
This is the acceleration of the runner
( a ) is the symbol for acceleration
It's a vector quantity in the direction of velocity change and measured in units
\[\vec a=\frac{\vec {∆𝜗}}{∆t}=\frac{\frac{m}{s}}{s}=\frac{m}{s^2}\]
A car moving at speed
\[5\;m/s\]
changed its speed to
\[15\;m/s\]
within a time of
\[10\;s\]
Then the average acceleration equals
What does the number
\[5 m/s\] \[......................\] mean to you?
What does the number
\[15 m/s\] \[......................\] mean to you?
What does the number
\[10 S\] \[......................\] mean to you?
How much did the velocity vector change?
\[......................\]
How much did the velocity vector change per unit time?
\[........................\]
Did you know you just calculated acceleration?
Click here to show solution
Acceleration Calculator
Acceleration Calculator
Initial Velocity (m/s):
Final Velocity (m/s):
Time Period (s):
When is motion accelerated and when is it decelerated?
There are two types of acceleration
Motion can be accelerated when the object's speed increases
Motion can be decelerated when the object's speed decreases
Acceleration Type
Acceleration Direction
Velocity Direction
Change in Velocity Vector
Accelerated Motion
Positive Direction
Positive Direction
Velocity Increases
Decelerated Motion
Negative Direction
Positive Direction
Velocity Decreases
Accelerated Motion
Negative Direction
Negative Direction
Velocity Increases
Decelerated Motion
Positive Direction
Negative Direction
Velocity Decreases
Important Results
Click here to show solution
In this simulation, motion with constant speed and variable speed
There are several controls below the experiment
The control at bottom left increases the number of repeated motions in different directions
Other controls adjust distance, time, position, speed and acceleration levels
Check the bottom icon to show repeated pictures of the object at equal time intervals
Set constant speed using points on the velocity graph and observe other graphs
Set increasing and decreasing speed using points on the velocity graph and observe other graphs
Relationship Between Slope of (Velocity-Time) Graph and Acceleration
The following graph shows the relationship between velocity and time for a bicycle
From the graph
Is the speed (constant - increasing - decreasing)?
Acceleration (uniform - zero - increasing - decreasing)
Calculate the acceleration if it exists
\[...................................................\]
Calculate the slope of the graph, what do you conclude?
\[...................................................\]
Compare between slope and acceleration, what do you conclude?
\[...................................................\]
Click here to show solution
Velocity-Time Graph Plotter
Velocity (m/s)
Time (s)
Motion Equations
When an object moves in one dimension, some move at constant speed while others move at uniformly changing speed
Object moving with uniformly changing speed
Object moving with constant speed
Acceleration is not zero \[𝑎≠0\]
Acceleration is zero \[𝑎=0\]
\[v_f=v_i+𝑎.t\]\[{v_f}^2={v_i}^2 + 2.𝑎(x_f-x_i)\]\[x_f=x_i+v_i.t+\frac{1}{2}.𝑎.t^2\]\[x_f=x_i+\frac{1}{2}({v_f}+{v_i}).t\]
\[X_f=X_i+v.t\]
1
A car started from rest with acceleration
\[4\;m/s^2\]
then the speed it reached after
\[6\;s\]
\[𝑣𝑓 = 10 \;\;m/s\;\;\;\;\;\;-C\]
\[𝑣𝑓 = 18 \;\;m/s\;\;\;\;\;\;-A\]
\[𝑣𝑓 = 12 \;\;m/s\;\;\;\;\;\;-D\]
\[𝑣𝑓 = 24 \;\;m/s\;\;\;\;\;\;-B\]
Click here to show solution
Choose the correct answer
2
An American football player moving at speed
\[10\;M/S\] was caught from
behind until he stopped within time
\[8\;S\]>Then the distance he covered
until stopping
\[∆𝑥 =20 \;\;m\;\;\;\;\;\;-C\]
\[∆𝑥 =10 \;\;m\;\;\;\;\;\;-A\]
\[∆𝑥 =30 \;\;m\;\;\;\;\;\;-D\]
\[∆𝑥 =40 \;\;m\;\;\;\;\;\;-B\]
Click here to show solution
Choose the correct answer
Adjusting Acceleration and Showing Velocity and Position Graphs
Free Fall
Motion Definition:
Motion of an object under Earth's gravity only without air resistance.
Free Fall Equations:
1. Final Velocity:
\[ v = v₀ + gt \]
g: gravitational acceleration
\[g ≈ 9.8\; m/s²\]
2. Vertical Displacement:
\[Δy = v₀t + ½gt²\]
3. Velocity without time:
\[v² = v₀² + 2gΔy\]
Study Purpose:
- Understand basics of motion with constant acceleration
- Analyze gravity's effect on objects
- Apply motion principles in engineering projects
Galileo Galilei:
First to scientifically study free fall in 17th century, proved objects accelerate equally despite mass differences (in vacuum).
Practical Applications:
- Parachute systems design
- Calculating object fall time in construction
- Programming space simulators
- Improving air sports performance
Practical Example:
If an object falls from 100 meters height:
Time to reach ground:
\[t = sqrt {\frac {2h}{g} }≈ 4.5 \;s\]
Impact velocity:
\[v = gt ≈ 44 m/s\]
Free Fall Calculator
Free Fall Calculator
Results:
Free Fall Experiment
In this simulation we'll determine free fall acceleration value for a ball in different universe regions
Acceleration\[𝑎=\frac{2∆Y}{t^2}\]
Time \[t (s)\]
Displacement \[∆Y(m)\]
Selected Location
\[𝑎=...........\]
\[t=...........\]
\[∆Y=..........\]
Earth
\[𝑎=...........\]
\[t=..........\]
\[∆Y=..........\]
Sun
\[𝑎=..........\]
\[t=...........\]
\[∆Y=...........\]
Moon
\[𝑎=...........\]
\[t=...........\]
\[∆Y=...........\]
Mars
\[𝑎=...........\]
\[t=..........\]
\[∆Y=..........\]
Jupiter
\[𝑎=...........\]
\[t=...........\]
\[∆Y=...........\]
Venus
Free Fall Experiment
Source
https://www.seilias.gr/go-lab/html5/diagrammataMetabalomenis.plain.html
Accelerated motion |
Sultan, Ahmed, and Majed
are three runners
Majed is moving with decreasing speed
Sultan is moving with constant speed
Ahmed with increasing speed
Which dot diagram represents each one's movement?
Which runner's speed is changing?
\[.................................\]An object moving with non-constant speed has acceleration
In a running race, consecutive pictures were taken every second
of runner 7 who was moving with constant acceleration
To calculate acceleration
First find the change in velocity vector
\[\vec {∆𝜗}=\vec {𝑣_𝑓}−\vec {𝑣_𝑖}\]
Then calculate the time rate
of velocity change
\[\vec a=\frac{\vec {𝑣_𝑓}−\vec {𝑣_𝑖}}{∆t}\]
This is the acceleration of the runner
( a ) is the symbol for acceleration
It's a vector quantity in the direction of velocity change and measured in units
\[\vec a=\frac{\vec {∆𝜗}}{∆t}=\frac{\frac{m}{s}}{s}=\frac{m}{s^2}\]
A car moving at speed
\[5\;m/s\]
changed its speed to
\[15\;m/s\]
within a time of
\[10\;s\]
There are two types of acceleration
Motion can be accelerated when the object's speed increases
Motion can be decelerated when the object's speed decreases
Acceleration Type Acceleration Direction Velocity Direction Change in Velocity Vector Accelerated Motion Positive Direction Positive Direction Velocity Increases Decelerated Motion Negative Direction Positive Direction Velocity Decreases Accelerated Motion Negative Direction Negative Direction Velocity Increases Decelerated Motion Positive Direction Negative Direction Velocity Decreases
The following graph shows the relationship between velocity and time for a bicycle
From the graph
Is the speed (constant - increasing - decreasing)?
Acceleration (uniform - zero - increasing - decreasing)
Calculate the acceleration if it exists
\[...................................................\]
Calculate the slope of the graph, what do you conclude?
\[...................................................\]
Compare between slope and acceleration, what do you conclude?
\[...................................................\]
When an object moves in one dimension, some move at constant speed while others move at uniformly changing speed
Object moving with uniformly changing speed Object moving with constant speed Acceleration is not zero \[𝑎≠0\] Acceleration is zero \[𝑎=0\] \[v_f=v_i+𝑎.t\]\[{v_f}^2={v_i}^2 + 2.𝑎(x_f-x_i)\]\[x_f=x_i+v_i.t+\frac{1}{2}.𝑎.t^2\]\[x_f=x_i+\frac{1}{2}({v_f}+{v_i}).t\] \[X_f=X_i+v.t\] A car started from rest with acceleration
\[4\;m/s^2\]
then the speed it reached after
\[6\;s\] \[𝑣𝑓 = 10 \;\;m/s\;\;\;\;\;\;-C\] \[𝑣𝑓 = 18 \;\;m/s\;\;\;\;\;\;-A\] \[𝑣𝑓 = 12 \;\;m/s\;\;\;\;\;\;-D\] \[𝑣𝑓 = 24 \;\;m/s\;\;\;\;\;\;-B\] Choose the correct answer An American football player moving at speed
\[10\;M/S\] was caught from
behind until he stopped within time
\[8\;S\]>Then the distance he covered
until stopping
\[∆𝑥 =20 \;\;m\;\;\;\;\;\;-C\] \[∆𝑥 =10 \;\;m\;\;\;\;\;\;-A\] \[∆𝑥 =30 \;\;m\;\;\;\;\;\;-D\] \[∆𝑥 =40 \;\;m\;\;\;\;\;\;-B\] Choose the correct answer Motion of an object under Earth's gravity only without air resistance. First to scientifically study free fall in 17th century, proved objects accelerate equally despite mass differences (in vacuum). If an object falls from 100 meters height: Acceleration\[𝑎=\frac{2∆Y}{t^2}\] Time \[t (s)\] Displacement \[∆Y(m)\] Selected Location \[𝑎=...........\] \[t=...........\] \[∆Y=..........\] Earth \[𝑎=...........\] \[t=..........\] \[∆Y=..........\] Sun \[𝑎=..........\] \[t=...........\] \[∆Y=...........\] Moon \[𝑎=...........\] \[t=...........\] \[∆Y=...........\] Mars \[𝑎=...........\] \[t=..........\] \[∆Y=..........\] Jupiter \[𝑎=...........\] \[t=...........\] \[∆Y=...........\] Venus
Click here to show solution
Then the average acceleration equals
What does the number
\[5 m/s\] \[......................\] mean to you?
What does the number
\[15 m/s\] \[......................\] mean to you?
What does the number
\[10 S\] \[......................\] mean to you?
How much did the velocity vector change?
\[......................\]
How much did the velocity vector change per unit time?
\[........................\]
Did you know you just calculated acceleration?
Click here to show solution
Acceleration Calculator
Important Results
Click here to show solution
In this simulation, motion with constant speed and variable speed
There are several controls below the experiment
The control at bottom left increases the number of repeated motions in different directions
Other controls adjust distance, time, position, speed and acceleration levels
Check the bottom icon to show repeated pictures of the object at equal time intervals
Set constant speed using points on the velocity graph and observe other graphs
Set increasing and decreasing speed using points on the velocity graph and observe other graphs
Relationship Between Slope of (Velocity-Time) Graph and Acceleration
Click here to show solution
Velocity (m/s)
Time (s)
Click here to show solution
Click here to show solution
Adjusting Acceleration and Showing Velocity and Position Graphs
Free Fall
Motion Definition:
Free Fall Equations:
g: gravitational acceleration
\[g ≈ 9.8\; m/s²\]
Study Purpose:
Galileo Galilei:
Practical Applications:
Practical Example:
Time to reach ground:
\[t = sqrt {\frac {2h}{g} }≈ 4.5 \;s\]
Impact velocity:
\[v = gt ≈ 44 m/s\]
Free Fall Calculator
Results:
Free Fall Experiment
In this simulation we'll determine free fall acceleration value for a ball in different universe regions
Free Fall Experiment
Source
https://www.seilias.gr/go-lab/html5/diagrammataMetabalomenis.plain.html
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