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# velocity problem

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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

#1
+1

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