#$&*
course Phy 231
9:00pm 8/29/2014
Video 1: Events- things that can be observed and measured
If A and B represent 2 events you can say that ΔA/ΔB = the Avg rate of change of A with Respect to B.
Video 2:
Problem:
car is at Mile Marker 15 at 8:00
car is at Mile Marker 318 at 1:00
A=miles
B=time
A with respect to B = ΔA/ΔB = Roc 303/5= 60.6 mph
Video 3:
Between 2 events.
Avg. Velocity is given by ΔAvg position/Δtime
Avg Acceleration is given by ΔAvg Velocity/Δtime
Instantaneous Velocity is a limit of Avg Roc on time intervals as time approaches 0. The time interval must contain the instant.
Instantaneous Acceleration is calculated in the same way.
Video 4:
v bar= Avg. Velocity= Δx/Δt
a bar= Avg. Acceleration= Δv/Δt
Avg velocity is represented by the difference quotient limit definition.
x(t+Δt)-x(t)/Δt which is = to the derivative dx(t)/dt
Avg acceleration is represented by the difference quotient limit definition.
v(t+Δt)-v(t)/Δt which is = to the derivative dv(t)/dt
Video 5:
change in t = Δt = t sub f - t sub 0
change in v = Δv = v sub f - v sub 0
calculate ""a"" bar with these values = Δv/Δt = slope = Avg acceleration
Avg acceleration is also the value at the midpoint of the graph if and only if the function is a line.
Video 6:
The ""graph trapezoid"" has 2 altitudes and a base
cut from the trapezoids midpoint to the higher side and place that triangle in the missing gap to create a perfect rectangle with the midpoint altitude and original base of the trapezoid, and and = area.
this area is approximate unless the trapezoid is perfect.
Video 7:
Splitting the function to get approximate areas will yield approximate Δx for the velocity function.
The more divisions used the more accurate the approximation is.
velocity is = to the approximate slope of the trapezoidal divisions
Definite Integrals will yield area or change in position.
Slope at a certain time gives acceleration.
Video 8:
Acceleration graphs work the same as the velocity graph in video 7.
With acceleration the area will represent Δv.
Definite Integrals will also yield this value as they did in video 7.
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Note that your Delta symbol is a special character and will not be represented correctly in a text form.
For this reason we use `d (a backward apostrophe and a lower-case d) to represent the Delta symbol.
If you do so your document will look like the following (done here by means of a simple search-and-replace):
Video 1: Events- things that can be observed and measured
If A and B represent 2 events you can say that `dA/`dB = the Avg rate of change of A with Respect to B.
Video 2:
Problem:
car is at Mile Marker 15 at 8:00
car is at Mile Marker 318 at 1:00
A=miles
B=time
A with respect to B = `dA/`dB = Roc 303/5= 60.6 mph
Video 3:
Between 2 events.
Avg. Velocity is given by `dAvg position/`dtime
Avg Acceleration is given by `dAvg Velocity/`dtime
Instantaneous Velocity is a limit of Avg Roc on time intervals as time approaches 0. The time interval must contain the instant.
Instantaneous Acceleration is calculated in the same way.
Video 4:
v bar= Avg. Velocity= `dx/`dt
a bar= Avg. Acceleration= `dv/`dt
Avg velocity is represented by the difference quotient limit definition.
x(t+`dt)-x(t)/`dt which is = to the derivative dx(t)/dt
Avg acceleration is represented by the difference quotient limit definition.
v(t+`dt)-v(t)/`dt which is = to the derivative dv(t)/dt
Video 5:
change in t = `dt = t sub f - t sub 0
change in v = `dv = v sub f - v sub 0
calculate ""a"" bar with these values = `dv/`dt = slope = Avg acceleration
Avg acceleration is also the value at the midpoint of the graph if and only if the function is a line.
Video 6:
The ""graph trapezoid"" has 2 altitudes and a base
cut from the trapezoids midpoint to the higher side and place that triangle in the missing gap to create a perfect rectangle with the midpoint altitude and original base of the trapezoid, and and = area.
this area is approximate unless the trapezoid is perfect.
Video 7:
Splitting the function to get approximate areas will yield approximate `dx for the velocity function.
The more divisions used the more accurate the approximation is.
velocity is = to the approximate slope of the trapezoidal divisions
Definite Integrals will yield area or change in position.
Slope at a certain time gives acceleration.
Video 8:
Acceleration graphs work the same as the velocity graph in video 7.
With acceleration the area will represent `dv.
Definite Integrals will also yield this value as they did in video 7.
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