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Position, Velocity, and Acceleration

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Regina Brown

on 24 November 2014

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Transcript of Position, Velocity, and Acceleration

Position, Velocity, & Acceleration
Regina Brown
Recall:
Applications using equations
Just by looking at a given position, velocity, or acceleration graph, it is possible to find the graphs of the non-given functions
f(x)=position
f'(x)=velocity
f''(x)=acceleration

Applications using graphs
example:
the position of a car is represented by the function f(x)=3t +5t+2. Find the car's instantaneous velocity and instantaneous acceleration at t=4 minutes.

2
answer:
f'(x)=6t+5
f'(4)=6(4)+5
f'(4)=29 m/s

f"(x)=6
f"(4)=6
f''(4)= 6 m/s
derive f(x) to find the velocity function
plug in 4 for t into f'(x)
solve --> don't forget units

derive f'(x) to find the acceleration funct.
plug in 4 for t into f''(x)
solve --> don't forget units
What you should know how to do
1. Derive/ Integrate to find the unknown functions (P,V, or A)
2. Use graphs to find the unknown functions (P,V, or A)
3. Find instantaneous acceleration & velocity
4. Find distance traveled after a certain amount of time

5. Find average velocity:

6. Find total distance traveled:

PVA Equations
PVA Graphs
Sources:
What can graphs and their derivatives tell us about P, V, A?
2
*If you are given just one equation, either derive or integrate to find the other two equations.
Position/ f(x)



Velocity/ f'(x)



Accel./ f''(x)
When given:
Tells us the:
This feature:
slope
concavity
concavity

value
slope
slope

value
value
Of this graph:
value
slope
value

slope
concavity
value

concavity
slope
f'(x)
f'(x)
f"(x)

f(x)
f(x)
f"(x)

f(x)
f'(x)
https://apstudent.collegeboard.org/apcourse/ap-calculus-ab/exam-practice
http://17calculus.com/calc04-linear-motion.php
https://secure-media.collegeboard.org/secure/ap/pdf/calculus-ab/ap-2009-calculus-ab-scoring-guidelines.pdf?__gda__=1387218710_9e52bb14a7e06fc9092d11bbe8a34d3e

f(x)
f'(x)
f"(x)
Derivation
Derivation
Example Problem:
Solution
Full transcript