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Mr. Rogers AP Physics C Study Guide -- Kinematics |
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Podcast (MP3 file):
Physics With Mr. R - The
Foundations of Classical Physics
Click
on the above link to hear Mr. Rogers discuss the foundations of
classical physics, including many of the subjects relevant to this
chapter (approximate play time = 17 minutes). For a transcript of the
above, click here (pdf file).
- MP3 file can be played using
Apple QuickTime. The download the latest version for free click
here.
- pdf files require an
Adobe® Acrobat® Reader® to view. You can download one for free
from by clicking
here.
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Copyright © 2006 T.K. Rogers, all rights reserved.
No part of the above podcast may be reproduced in any form, electronic or
otherwise, without express written approval.
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| Basic Mathematical
Definitions |
Equations for Constant Acceleration
(Note: The 2 equations listed below only work
for constant acceleration) |
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speed = (distance) / (time) |
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x = 1/2at2 + vot + xo |
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a = dv/dt |
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v = at + vo |
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v = dx/dt |
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| Calculus -
derivative of a polynomial |
Calculus -
integration of a polynomial |
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Finds the slope at a
point |
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Finds the area under a curve |
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∫u xn
dx = u/(n+1) x (n+1) + C for n!=1 |
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Assume planet Earth and
no air resistance for the following:
- Derivative: the slope at a point.
- Integral: the area under the curve
between two values.
- The negative sign on a vector indicates
direction. It does not indicate that an object is slowing down.
- How to determine if an object is
slowing down or speeding up:
- Speeding up: the acceleration vectors
go in the same direction
- Slowing down: the acceleration vectors
go in opposite directions.
- Acceleration due to Gravity: On the surface of a planet, objects all
fall at the same acceleration if air resistance is negligible,
regardless of their mass.
- Drop an object, throw it up, throw it
down and it still accelerates at the same rate, 9.8 m/s/s downward.
- Throw an object upward and it will reach
zero velocity at the top of its path but the acceleration is still 9.8
m/s/s downward.
- Models: Physics is about model building. Models
always have errors due to simplifying assumptions.
- Freefalling objects: ignoring air resistance,
free falling objects accelerate downward with a rate = g. By definition,
they only have a force of gravity acting on them.
- Effects of air resistance on a dropped object:
The velocity starts at zero and reaches a constant value called terminal
velocity. The acceleration starts at one g and goes to zero at terminal
velocity
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| Coin Flip Problem:
Albert flips a coin up in the air at an upward velocity of
5 m/s. He fails to catch it on the way down and it falls down an 8 m deep
well. Draw a vs t, v vs t, and y vs t curves. Calculate the max height and
max magnitude of velocity of the coin. |
Batmobile Problem: Batman
fires up the the Batmobile and roars off with an acceleration = 5t +
10. Draw the a vs t and v vs t plot. Find the final velocity of Batman
and how far he travels in 2 seconds. |
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Falling With Air Resistance:
Compare the the a vs.t, v vs. t, x vs. t curves
with air resistance to those without for a dropped object. |
Two-Part Kinematics Problem:
Starting from rest
Martha accelerates her motor cycle forward at 5 m/s2 for
ten seconds then accelerates backwards at 2 m/s2 for ten
seconds. How fast is she going at the end of the 20 second time span
described above? How far has she traveled? Sketch the
a vs.t, v vs. t, x vs. t graphs. |
| Graphical
Integration: Given a graph of acceleration vs. time solve for
velocities and displacements. |
Graphical Derivatives: Given a graph of
displacement vs. time solve for velocities and accelerations. |
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| acceleration
(vector) |
frame of
reference |
speed (scalar) |
| derivative |
integration |
scalar |
| displacement
(vector) |
kinematics |
velocity
(vector) |
| distance (scalar) |
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