Collin Wiley PLUS Chegg C edugen.wileyplus.com Gradebook ORION Home Read, Study

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Collin Wiley PLUS Chegg C edugen.wileyplus.com Gradebook ORION Home Read, Study & Practice Assignment Assignment Open Assignment FULL SCREEN PRINTER VERSION BACK ONEXTD ASSIGNMENT RESOURCES Chapter 02, Problem 119 Homework 2 Fall The position of a particle as it moves along a y axis is given by 2015 V Chapter 02 Problem y 3,0cm in 4), 022 SN Ch ter 02, Prob with t in seconds and y in centimeters. (a) What is the average velocity of the particle between t-0 and t 2.0 s? b) What is the instantaneous velocity of the particle at t 0, 1.0, and 025 2.0 s? (c) What is the average acceleration of the particle between 0 and t 2.0 s? d) What is the instantaneous acceleration of the particle at t 0, 1.0, and 2.0 s? 02, Prob 029 (a) Number Units 02, Prob 033 2.0s 02, Prob 035 (b) Number Units e Chapter 02, Problem 049 c) Number Units 02, Prob 054 SN 2.0s 02, Prob (d) Number Units 069 02, Prob 088 02, Prob 099 02, Prob Question Attempts: 0 of 5 used SAVE FOR LATER SUBMIT ANSWER 090 02, Prob 119 V Chapter 03 Problem 009 Copyright 2000-2015 by ter 03, Prob ghts y & S Ch Chapter 03 Problem License Agreement l Privacy Policy I G 2000-2015 John Wiley & Sons Inc. All Rights Reserved. A Division of John Wiley Sons Inc. Version 4.16.1.7 9/3/2015

Explanation / Answer

y = 3*sin(pi*t/4)

1)
Distance Travelled at t=0
y = 3*sin(pi*0/4)
y = 3*sin(0)
y = 0
Distance Travelled at t= 2
y = 3*sin(pi*2/4)
y = 3*sin(pi/2)
y = 3* 1
y = 3 cm

Average Velocity between t=0 and t=2 is Distance Travelled/ Time
= 3/2 = 1.5 cm/sec

2) Instantanious velocity at all t can be represented by :
d(y)/dt = d(3*sin(pi*t/4))/dt
d(y)/dt = 3*(pi/4)*cos(pi*t/4)
v = 3*(pi/4)*cos(pi*t/4)
i) t=0
v = 3*(pi/4)*cos(pi*t/4)
v = 3*(pi/4)*cos(0)
v = 3*(pi/4)*1
v = 2.3571 cm/sec

ii) t=1
v = 3*(pi/4)*cos(pi*t/4)
v = 3*(pi/4)*cos(pi/4)
v = 3*(pi/4)*0.7071
v = 1.666 cm/sec

iii) t = 2
v = 3*(pi/4)*cos(pi*t/4)
v = 3*(pi/4)*cos(pi/2)
v = 3*(pi/4)*0
v = 0 cm/sec

3) Average acceleration between t=0 and t=2
Acceleration (a) can be defined as d(v)/dt where v = 3*(pi/4)*cos(pi*t/4) as derived in the above step.
a = 3*(pi/4)*(pi/4)*(-sin((pi t)/4))
d/dt(3/4 pi cos((pi t)/4)) = -3/16 pi^2 sin((pi t)/4)

a(0) = -3/16*pi^2*sin((pi*0)/4)
a(0) = -3/16*pi^2 *0 = 0

a(2) = -3/16*pi^2*sin(pi/2) = -1.850

Average acceleration = -1.850/2 = - 0.925 cm/sec^2

4)
a(t) = 3*(pi/4)*(pi/4)*(-sin((pi t)/4))
a(0) = 0
a(1) = -1.308
a(2) = -1.850

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