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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 = 3 sin(πt) + 4 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

 Apr 23, 2020
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plug in  t= 1       to find s = displacment = -4 cm

  @       t = 2                  s = +4

 

So in one second from   1  to 2    displacement   chages by   8           average velocity is   8 cm / 1 sec   = 8 cm/sec

 

do similar for the other time frames

 

 

b.   since it asks for an estimate.....try to estimate the slope of the equation at t= 1

                it is negative  

        it is NEARLY a straight line between  t = .5   (value ~ 3)  to  t = 1   (value = -4)

              slope =     ( 3 - - 4) / (.5 - 1) =  -7/.5 = -14

 

     approx -14 cm/sec

 

 

Here is a desmos graph which ma help you ....

https://www.desmos.com/calculator/fkg8uqs8z0

 Apr 23, 2020
edited by ElectricPavlov  Apr 23, 2020
edited by ElectricPavlov  Apr 23, 2020

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