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The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion 

s = 5 sin(πt) + 2 cos(πt),

 where t is measured in seconds. (Round your answers to two decimal places.)

a) Find the average velocity during each time period.

(i)    [1, 2] 
 cm/s 

(ii)    [1, 1.1] 
 cm/s 

(iii)    [1, 1.01] 
 cm/s 

(iv)    [1, 1.001] 
 cm/s 


(b) Estimate the instantaneous velocity of the particle when t = 1. 
 cm/s

 Jan 26, 2018
edited by Guest  Jan 26, 2018
 #1
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The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion 

s = 5 sin(πt) + 2 cos(πt),

 where t is measured in seconds. (Round your answers to two decimal places.)

\(s = 5 sin(\pi t) + 2 cos(\pi t)\\ \frac{ds}{dt}=v(t)=5\pi cos(\pi t)-2\pi sin(\pi t)\)

 

a) Find the average velocity during each time period.

(i)    [1, 2]  cm/s     

\(s(t) = 5 sin(\pi t) + 2 cos(\pi t)\\ s(1) = 5 sin(\pi ) + 2 cos(\pi )=-2\\ s(2) = 5 sin(2\pi ) + 2 cos(2\pi )=0+2=2\\ Average\;\; velocity = \frac{2--2}{2-1} =4cm/sec\)

(ii)    [1, 1.1]  cm/s 

(iii)    [1, 1.01]  cm/s 

(iv)    [1, 1.001]  cm/s 


(b) Estimate the instantaneous velocity of the particle when t = 1. 
 cm/s

\(v(1)=5\pi cos(\pi )-2\pi sin(\pi )=-5\pi-0=-5\pi\;cm/sec\)

 

You can do the others yourself :)

 Jan 26, 2018

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