Position Function, Velocity and Acceleration

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Position Function, Velocity and Acceleration
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Consider a graph of displacement (distance
traveled) vs. time.
Average velocity can be found by taking
The speedometer in your car does not measure
average velocity, but instantaneous velocity.
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Start with a position function.
Distance s f(t)
Velocity is the first derivative of position.
Velocity v
Acceleration is the second derivative of position.
Acceleration a
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Example
Free Fall Equation
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example
If distance is in
Velocity would be in
Acceleration would be in
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It is important to understand the relationship
between a position graph, velocity and
acceleration
acc neg vel pos decreasing
acc neg vel neg decreasing
acc zero vel neg constant
acc zero vel pos constant
acc pos vel neg increasing
velocity zero
acc pos vel pos increasing
acc zero, velocity zero
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Example A yo-yo moves along a straight line up
and down. Its height above the ground, as a
function of time is given by the function H(t)
t3 - 6t2 5t 30. Where t is in seconds and H(t)
is in inches. 0,4
Find H(0) Find H(4)
V(t)
A(t)
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Graph all three functions on your calculator.
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Find the maximum height.
Find the minimum height.
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Find the total displacement of the yo-yo. (Total
displacement is defined as the final position
minus the initial position.
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Find the average velocity for the time period.
Find the velocity at t 1 second.
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Find the maximum velocity.
Find the minimum velocity.
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Over what time periods is the yo-yo
accelerating? Decelerating?
When is there no acceleration? What is this
point on the position function called?
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