The position of an object moving along a line is given by $p(t) = sin(3t- pi /4) +3$ . What is the speed of the object at $t = (3pi) /4$ ?

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Answer 1 · 2017-06-08T04:32:47

The speed is $=3$

The speed is the derivative of the position

$p(t)=sin(3t-1/4pi)+3$

$v(t)=3cos(3t-1/4pi)$

When $t=3/4pi$ , we have

$v(3/4pi)=3cos(3*3/4pi-1/4pi)$

$=3cos(9/4pi-1/4pi)$

$=3cos(8/4pi)$

$=3cos(2pi)$

$=3*1$

$=3$

The position of an object moving along a line is given by p(t) = sin(3t- pi /4) +3 p(t) = sin(3t- pi /4) +3 . What is the speed of the object at t = (3pi) /4 t = (3pi) /4 ?