Simulation of Constant Velocity Compared to Constant Acceleration http://higheredbcs.wiley.com/legacy/college/h
alliday/0471320005/simulations6e/index.htm?newwindow=true
Average Acceleration = Change in Velocity
Time Interval
a = v t
a = v2 - v1
t2 – t1
Average Acceleration
Instantaneous Acceleration
Instantaneous Acceleration is the acceleration at a given instant.
Can you always tell if you are accelerating while observing the speedometer of a car?
Questions:
1. If you are riding on a merry-go-round at a constant speed of 2m/s are you accelerating?
2. When you are riding in a car at a constant speed of 5mph turning right, are you accelerating?
Deceleration
Deceleration is acceleration that causes the velocity’s magnitude to be reduced.
Is it necessary for deceleration to be negative?
Example 1: “The Bee” A bee is flying in the air with an initial velocity of
+0.5 m/s. It then accelerates for 2.0 s to a velocity of +1.5m/s.
1. Draw a motion diagram.
2. Draw a vector diagram showing the initial and final velocity and the acceleration of the bee.
3. Calculate the acceleration of the bee.
Answer: +0.5m/s2
Example 2
The bee decides to slow down from +1.75m/s to +0.75m/s in 2s.
1. Draw the motion diagram.
2. Draw the vector diagram.
3. What was the acceleration of the bee?
Answer: -0.5m/s2
Example 3: Susan slides on the icy sidewalk with an initial
velocity of 2m/s. She slows down for 3s at 0.5m/s2.
Draw the vector diagram. What is her final velocity?
Answer: 0.5m/s
Example 1: Position vs Time
Time (s)o
Position (m)
Parabola
1. What is the slope of the tangent to the curve at t=0s?
2. Is the slope of the tangent to the curve increasing or decreasing with increasing time?
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Note:
The slope of the tangent to the curve at a given time of the position-time graph is the instantaneous velocity.
Velocity vs Time
Time (s)
o
Velocity (m/s)
•Slope of Line= Acceleration
•Area Under Line=Displacement (Change in Position)
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The slope of the line of the velocity- time graph is the instantaneous acceleration.
For constant acceleration that slope also equals the average acceleration.
For motion with varying acceleration, the velocity graph would be a curve. The slope of the tangent to the curve at a given time would represent the instantaneous acceleration.
Example 2: Position vs Time
Time (s) 5s
o
Position (m)Parabola
1. What is the slope of the tangent to the curve at t=5s?
2. Is the slope to the tangent, positive or negative at t=0 s?
3. Is the slope of the tangent, increasing or decreasing with increasing time?
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Note:
• Area Under Line of the velocity-time graph =Displacement (Change in Position)
• Area under the line of the acceleration-time graph =Change in Velocity