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 changing?
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
Good. This is correct.
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 change in position / change in clock time, which is the average rate of change of position, not velocity.
You need to follow the scheme outlined in the preceding problem to get the requested result.
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
Determine the length of a pendulum whose period is 1.474212s:
1.47212 = .0906L - .0084
The function is T^3 = .0906 L - .0084. So this should read
1.47212^3 = .0906L - .0084
.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