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course Phy 231
Assignment 2 Prob 1_2 V 4_7#$&*
course Phy 231
2/11 11My answers are in between
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####"" ""ASSIGNMENT 2 PROBLEM 1 VERSION 4
If the velocity of the object changes from 3 cm / sec to 13 cm / sec in 7 seconds, then at what average rate is the velocity changing?
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Average rate of velocity change = 'delta v / 'delta t = (13 - 3) (cm / s) / 7s = (1.43 cm/s) / s
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A ball rolling from rest down a constant incline requires 9.6 seconds to roll the 99 centimeter length of the incline.
What is its average velocity?
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average Velocity = 'delta s / 'delta t = 99 cm / 9.6 s = 10.3125 cm/s = 10 cm/s
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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?
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average velocity = 'delta v / 'delta t
v final = 2 * average velocity
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Good.
'This ball' refers to the ball of the present situation, whose average velocity is 10 cm/s.
So the full answer to this question would include the fact that this ball has a final velocity of 20 cm/s.
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v final = 2 * 10 cm/s = 20 cm/s
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What average rate is the velocity of the ball therefore changing?
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average rate of velocity change = (v_final - V_intial) / 'delta t
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This still refers to the same ball, and it also requires a quantitative answer.
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An automobile accelerates uniformly down a constant incline, starting from rest. It requires 16 seconds to cover a distance of 120 meters. At what average rate is the velocity of the automobile therefore changing?
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v_ave = 'delta s / 'delta t = 120m / 16s = 7.5 m/s
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This is the average velocity. You need this, but it doesn't answer the question.
The question asks for the average rate at which the velocity is changing.
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Average Rate Of Velocity Change = 'delta Velocity / 'delta time = (20 cm/s - 0 cm/s) / 9.6 s = 2.1 cm /s / s
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This would apply to the ball, and it is correct.
However at this point the question is asking about the car.
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ASSIGNMENT 2 PROBLEM 2 VERSION 7
For a certain pendulum, periods of T = .36, .5111941, .6275753 and .7258872 seconds are observed for respective lengths L = 9, 18, 27 and 36 units.
Determine whether the transformation T -> T2 or T -> T3 linearizes the function better.
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T -> T2 = (T2 - T1) / ( L2 - L1) = (.5111941 - .36 )s / ( 18 - 9 ) L units = 0.017 s/ Lunit
T -> T3 = (T3 - T1) / ( L3 - L1) = (.6275753 - .36 )s / ( 27 - 9 ) L units = 0.015 s/ Lunit
T -> T2 Linearizes the function better it is steeper.
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Determine the equation of the resulting straight line, and solve the equation for T.
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m = 'delta t / 'delta L, 'delta t = m * 'delta T = (0.017 s/ Lunit) * 9 Lunit = 0.153 sec
'delta t = 0.15
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Use your equation to determine the period of a pendulum whose length is 21.21293 units.
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m = 'delta t / 'delta L
0.015 s/ Lunit = 'delta t * 21.21293 Lunits
'delta t = 0.015 * 21.21293 = 0.32 seconds
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Use your equation to determine the length of a pendulum whose period is 1.334508 seconds.
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m = 'delta t / 'delta L
'delta L = 'delta t / m = 1.334508 seconds / 0.015 seconds / Lunit = 89 units ""
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Good, but you need to answer that one question about average rate of change of velocity.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
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For that car the requested average rate would be a little less than 1 m/s^2.
Be sure you understand how to reason this out. If so, there's no need for a revision.
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