Question 1118715
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            Since the velocity has opposite directions in different time moments,  the question  "when the velocity is maximal ?" 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;has NO much sense &nbsp;(if any).  &nbsp;Much more reasonable question is &nbsp;"when the &nbsp;<U>magnitude</U> &nbsp;of the velocity is maximal ?"



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1.  Maximum velocity <U>magnitude</U> is when  {{{cos(3*pi*t)}}} = +/- 1, i.e. when 

    {{{3pi*t}}} = {{{k*pi}}},


    where "k" is any integer.  First such a moment happens when  k = 0,  t = 0.

    At this time moment velocity is  -3 feet per second, and the velocity magnitude is 3 feet per second.


    Next such a moment happens when  t = {{{1/3}}} of a second.

    At this time moment velocity is  3 feet per second, and the velocity magnitude is again 3 feet per second.




2.  In the highest position the vertical velocity is equal to 0 (zero).


    In the lowest position the vertical velocity is equal to 0 (zero), again.


    It happens if and only if  {{{cos(3*pi*t)}}} = 0,  i.e.  {{{3*pi*t}}} = {{{pi/2 + k*pi}}},  or  t = {{{1/6 + k/3}}},  where k is any integer.


    Two such sequential time moments are t = {{{1/6}}}  of a second  and  t = {{{1/6+1/3}}} = {{{1/2}}} of a second with the difference between them of  {{{1/3}}} seconds. 
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