AP "C" Physics
Summer Assignment---1st quiz!
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AP formula sheet
Test Date : May 14, 2018
Letters/Folders
Grading Scheme50% Unit Tests
25% Lab Reports
20% Quizzes
5% Homework
Freefall - ball tossx
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Freefall - ball tossx
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Freefall
UP DOWN- ∆ speed + ∆ speed- direction + direction
Chapter 2 Motion in One DimensionAve Velocity:x
tti tf
xi
xfAverage Velocity from t i to tf is equal to the slope of the straight line joining inital and final positions
V = displacement∆t
Constant Acceleration
v = dt
v = vf + vi2
1(vf + vi)t2d = vt
a = vf vit
d =
t = vf via
vf = vi + at
d = 1(vf + vi)2
vf via
vf2 = vi2 + 2ad
1((vi + at) + vi)t2
d =
d = vit + at212
Instantaneous Velocity(the velocity of a particle at any instant of time)
as ∆t approaches 0
This is the "derivative" of x with respect to t
2.6 The slope of a dt graph will determine the velocity.
The slope of a vt graph will determine the acceleration!
But what happens if the slope is changing?
THE DERIVATIVE! The slope as t > 0
example:
The derivative of a sum is the sum of the derivatives!
Chain Rule! When there is a function inside a function!
Take the derivative of the "outside" X derivative of the "inside".
The derivative of a product: the derivative of the first X the 2nd
+ the derivative of the 2nd X the1st
A proton moves along the X axis according to the equation: * meters and seconds
Determine its velocity and acceleration after 3 seconds
Try these:
= ?
Chain Rule ReviewWhen taking the derivative of a function of a function
f(g(x))f(g(x))' = f'(g(x))(g'(x))
dfdx =
dfdg
dgdx
Examples:
(x3 3x)2 sin((x+4)2) (x3 x2)1
set g(x) = u
Examples:
(x3 3x)2 sin((x+4)2)
(x3 x2)1
Integration
Also labeled the antiderivative
Inverse to differentiation (just like multiplication/division)
"Reverses" differentiation
Gives the sum total of a quantity , adding infinitesimally small areas
Rules for Integration different than derivatives
Geometry Calculusarea under the line = displacement
area under the curve = displacemen (the integral)
slope of the line = acceleration derivative of the velocity = instantaneous acceleration
Displacement from a Vt graph as a function of time:
top final
bottom initial
"power rule" for integration
Integral of the sum
=
Sum of the integrals
Product Rule for integration >> difficult
called integration by parts
Will also need to use usubstitution
We will go over it as we need it
But PAY ATTENTION in your math course when you get to it!!!!
How to find "C" After an indefinite integral we compensate for any missing constants by adding an unknown constant "c" to our answer
"c" can be found from initial conditions (boundry conditions)
ti = 2s, xo = 5m, vo = 1.2 m/s examples of initial
Plug in initial conditions to equations to find c (c should be the only variable)
If initial conditions are given, it is implied that you must solve for the constant
conditions
example:Find the displacement as a function of time
given: V = 3t
= ?
Vector NotationResolve each vector into x, y and z components
Often given UNIT VECTOR notation to specify a given direction
i, j, k
A = Axi + Ayj B = Bxi + Byj
R = A + B R = (Ax + Bx)i + (Ay + By)j
magnitudedirection magnitude direction
Add Vectorally!
A = 3i + 4j B = 5i + 6j C = 7i 10jFind the magnitude and direction of each vector
Find the following resulting vectors
A + B A C B C C A
A = 3i + 4j B = 5i + 6j C = 7i 10jFind the magnitude and direction of each vector
Find the following resulting vectors
A + B = (3 5)i + (4 + 6)j = 2i + 10j
A C = (3 7)i + (4 + 10)j = 4i + 14j
B C = (5 7)i + (6 +10)j = 12i +16j
C A = (7 3)i + (10 4)j = 4i 14j
Recall Dot Product or SCALAR Product
i i = j j = k k = 1
i j = 0
We will also do the Cross or VECTOR Product later on
only when you multiply like components (i.e. parallel to one another) will you get a
result
A B = AxBx + AyBy + AzBz
ProjectilesTime to reach the top:
ProjectilesFull Range:
section 4.7
Centripetal Acceleration
Circular Motionar = time rate of change in direction of velocity
at = time rate of change in the speed of the object
angular displacement
average angular velocity
**Every point has the same angular velocity!!!!!!!!
BUT may have different linear velocity!!
section 4.7
Centripetal Acceleration
linear => angular *every point has same angular velocity
* not every point has the same linear velocity
1 radian> the angle subtended byan arc length equal to the radius of the arc.
