course Phy 201
You did a good job with all but the last part of the first quiz. The parts you got right illustrate how to find the average rate of change of velocity. See if you can apply this method to the last part of the first quiz.
When you substitute T into an equation with T^3, this means you have to cube T. And when the equation is for T^3, then to solve for T you have to take a cube root. See my note on the second quiz.
On the third quiz your method is good, but where you should have used initial velocity you used something else. See my note.
I believe you'll be able to correct these problems without much trouble, but if not send me questions.
Otherwise send me revisions as necessary.
Assignment 2 Problem 1 recalculation
If the velocity of the object changes from 5 cm / sec to 14 cm / sec in 9 seconds, then at what average rate is the velocity ch
Avg. Velocity of an object that changes from 5cm/s to 14cm/s in 9s is (14cm/s ?5cm/s) / 9s = 1cm/s/s
It requires 5.1 seconds, starting from rest, for a ball to roll the 38 centimeter length of a uniform incline.
?What is its average velocity?
Avg. Velocity of a ball that rolls 38cm in 5.1s is = 38cm / 5.1s = 7.5cm/s
An object which accelerates uniformly from rest will attain a final velocity which is double its average velocity.
?What therefore is the final velocity of this ball?
Final Velocity is double the average velocity so 7.5cm/s * 2 = 15cm/s
?What average rate is the velocity of the ball therefore changing?
Final vel. ?initial vel. / time elapsed = 15cm/s / 5.1s = 2.94cm/s/s
At what average rate does the velocity of an airplane change, if it accelerates uniformly down a runway, starting from rest, requiring 10 seconds to cover a distance of 154 meters.
154m / 10s = 15.4m/s is the average rate that the velocity of the airplane changes
This is the average rate of change of position, not the average rate of change of velocity.
How do you find the average rate of change of velocity?
Assignment 2 Problem 2 version 3
For a certain pendulum, periods of T = .708, .8943636, 1.02536 and 1.129783 seconds are observed for respective lengths L = 4, 8, 12 and 16 units.
?Determine whether the transformation T -> T2 or T -> T3 linearizes the function better.
?Determine the equation of the resulting straight line, and solve the equation for T.
?Use your equation to determine the period of a pendulum whose length is 21.87513 units.
?Use your equation to determine the length of a pendulum whose period is 1.474212 seconds.
T^3 linearizes the function better.
The equation for a straight line from the graph of T^3 v/s Length is T^3 = .0906L - .0084.
Determine the period of a pendulum whose length is 21.87513 units:
T^3= .0906 (21.87513) - .0084
T^3 = 1.973487 periods
You need to solve this for T. Take the cube root of both sides. You'll get something like T = 1.2 or 1.3 (likely something between those values).
Determine the length of a pendulum whose period is 1.474212s:
1.47212 = .0906L - .0084
The formula is T^3 = .0906L - .0084. This means that the given value of T must be cubed before you solve the rest of the equation.
.0084 + 1.47212 = .0906L
1.474212 / .0906 = L
L = 16.36437 units is the length of the pendulum.
Assignment 3 version 9
An object travels a distance of 32 cm in 17.6 seconds from start to finish. If its acceleration is uniform and its initial velocity zero, then what are its average velocity, acceleration and final velocity?
Average Velocity = 32cm / 17.6s = 1.82cm/s
Final Velocity = vAve * 2 = 1.82cm/s*2 = 3.64cm/s
Acceleration = Final vel. ?initial vel. / Time interval = (3.64-1.82cm/s) / 17.6s = 0.103cm/s/s
The initial velocity of the object is not 1.82 cm/s. How fast is the object moving at the instant it is released?