course phy 201
20090911 1927
1.� State the definition of rate of change.vvvv
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Rate of change is the average rate of change of [A] with respect to [B].
&#Good work. &#
2.� State the definition of velocity.
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Velocity is the ave. roc of position wrt clock time.
3.� State the definition of acceleration.
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Acceleration is the ave. roc of average velocity wrt clock time. (e.g., cm/s^2
&#Good responses. &#
4.� A ball rolls along a path, moving from position 20 cm to position 50 cm as its velocity increases from 5 cm/s to 15 cm/s.
What is its change in velocity and how do you obtain it from the given information?� S1- 50 cm, S0 - 20 cm, V1 - 15 cm/s, V0 - 5 cm/s
&&&& change in velocity ~ V1-V0 = 15 cm/s - 5 cm/s = 10 cm/s (knowing initial and final velocities, subtracting the two (vf-v0) gives
the result of the change in velocity)
What is its change in position and how do you obtain it from the given information?� &&&& change in position ~ s1 - s0 = 50cm - 20cm
= 30cm (Knowing the initial and the final positions the ball travels on the path, we are able to obtain the displacement by
subtracting the final minus the initial velocity)
5.� A ball accelerates from velocity 30 cm/s to velocity 80 cm/s during a time interval lasting 10 seconds.
Explain in detail how to use the definitions you gave above to reason out
the average velocity of the ball during this interval, &&&& ave velocity is the average roc of position wrt to clock time
and
its acceleration during this interval.� &&&& acceleration is the average roc of velocity wrt to clocktime
Remember, the main goal is to use a detailed reasoning process which connects the given information to the two requested results.�
You should use units with every quantity that has units, units should be included at every step of the calculation, and the algebraic details of the units calculations should be explained.
Your explanations are good, but they don't include all the details. You should actually do the calculations, applying the explanations.
6. �A �graph trapezoid� has �graph altitudes� of 40 cm/s and 10 cm/s, and its base is 6 seconds.� Explain in detail how to find each of
the following:
The rise of the graph trapezoid.� &&&& Rise of the trapezoid would be 40 cm/s and 10 cm/s - for the average rise (or velocity),
subtract 10 cm/s from 40 cm/s and divide by two. the rise with be parallel to the y-axis and perpendicular to the x-axis
The run of the graph trapezoid.� &&&& the run (or base) of the trapezoid would be the measurement (units) between the two altitudes
(initial and final. the run will be located on or parallel to the x-axis
The slope associated with the trapezoid.� &&&& the slope will be located between the two altitudes (initial and final) this slope
will be the altitudes (average) divided by the run (base) // rise/run
The dimensions of the equal-area rectangle associated with the trapezoid.� &&&& if the trapezoid were to be made so that a perfect
square (figure) or a rectangle with two, two equal lengthed sides could be taken out of the trapezoid to leave a triangle (""sitting""
on top of the ""box""), then the dimension of the rectangle could be found with one side being the base (or run of the trapezoid),
another side being the difference in velocity (v1-v0), and the third (being the hypotenuse) could be find by A(square)[base]+B
(square)[`dV]=C(square)
The area of the trapezoid. &&&& V0`dt+.5(V1-V0)`dt OR [(V1+V0)/2]`dt
The first equation is solved by first finding the area of the square (or rectangle) and then adding it to the area of the triangle
(which could be visualized splitting the trapezoid along the parallel line that is perpendicular to the initial velocity) OR
The second equation is simply taking the midpoint of the slope ((v1-v0)/2) and multiplying it into the base (or change in clock time
- time interval). This can be visually seen by making a square (or rectangle) out of the trapezoid by flipping the upper portion
that is left from a parallel (to the base) ""cut"" from the midpoint of the slope assuming the line is linear.
Each calculation should include the units at every step, and the algebraic details of the units calculations should be explained.
This also needs to include calculations with the actual quantities given in the problem.
7.� If the altitudes of a �graph trapezoid� represent the initial and final positions of a ball rolling down an incline, in meters, and the based of the trapezoid represents the time interval between these positions in seconds, then
What is the rise of the graph trapezoid and what are its units?� &&&& rise is the changes in position in units of meters
What is the run of the graph trapezoid and what are its unit?� &&&& run is the change of clock time in units of seconds
What is the slope of the trapezoid and what are its units?� &&&& the slope is the average roc of position wrt to clock time (which is velocity) - units of m/s
good
What is the area of the trapezoid and what are its units?� v1+v0 (m/s)/2 * `ds &&&& area is the ave roc of velocity wrt to clock time which would be in unts of m/s(squared)
this isn't correct
What, if anything, does the slope represent?� &&&& could represent average velocity (or change in velocity)
it's one of the two, but the two or different, so whichever one it is, it isn't the other
What is the altitude of the equal-area rectangle and what are its units?� &&&& altitude of the equal-area rectangle would represent the average of the two positiosn; units would be in meters
What is the base of the equal-area rectangle and what are its units?� &&&& base is the change in clock time and in units of seconds
What, if anything, does the area represent?� &&&& multiplying meters * seconds would come out as cm*s which does not represent anything.
good
Each answer should include a complete explanation, reasoned out from the geometry of the trapezoid and the definitions you gave at the beginning.
8.� If the altitudes of a �graph trapezoid� represent the initial and final velocities of a ball rolling down an incline, in meters / second, and the based of the trapezoid represents the time interval between these velocities in seconds, then
What is the slope of the trapezoid and what are its units?� &&&& slope - rise/run = (vf+v0)/2)/`dt and would be measured in cm/s(squared)
What is the area of the trapezoid and what are its units?� &&&& area - altitude * base = ((Vf+V0)/2)*`dt with a unit as cm (cm/s * s
What, if anything, does the slope represent?� &&&& slope of the trapezoid is average acceleration
What, if anything, does the area represent?� &&&& the area of the trapezoid is the change in position
Each answer should include a complete explanation, reasoned out from the geometry of the trapezoid and the definitions you gave at the beginning.
9.� A ball rolls along a path, moving from position 20 cm to position 50 cm as its velocity increases from 5 cm/s to 15 cm/s.
If its acceleration is uniform, then how long does this take, and what is the ball�s acceleration?� ��&&&& change in position - 30cm,
change in velocity - 10 cm/s, change in time - 30cm/(10cm/s) = 3 seconds. It takes the ball 3 seconds to roll down the path.
Acceleration - `dv/`dt = 10cm/s / 30 s = .333 cm/s^2. the ball travels at an average of .333 centimeters per squared seconds.
Excellent, but as you said already the time interval is 3 sec, not 30 sec, so you get 3.33 cm/s^2.
You're OK here. It looks like you've got it.