### Present Remotely

Send the link below via email or IM

• Invited audience members will follow you as you navigate and present
• People invited to a presentation do not need a Prezi account
• This link expires 10 minutes after you close the presentation

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

# Position, Velocity, and Acceleration

No description
by

## Regina Brown

on 24 November 2014

Report abuse

#### 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
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