The position of an object moving along a line is given by $p(t) = sin(2t- pi /3) +2$ . What is the speed of the object at $t = (2pi) /3$ ?

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Answer 1 · 2016-05-10T12:03:25

$v((2pi)/3)=-2$

$v(t)=d/(d t) p(t)$

$v(t)=d/(d t)(sin(2t-pi/3)+2)$

$v(t)=2*cos(2t-pi/3)$

$"for "t=((2pi)/3) rarr v((2pi)/3)=2*cos(2*(2pi)/3-pi/3)$

$v((2pi)/3)=2*cos((4pi)/3-pi/3)$

$v((2pi)/3)=2*cos pi$

$cos pi=-1$

$v((2pi)/3)=-2*1$

$v((2pi)/3)=-2$

The position of an object moving along a line is given by p(t) = sin(2t- pi /3) +2 p(t) = sin(2t- pi /3) +2 . What is the speed of the object at t = (2pi) /3 t = (2pi) /3 ?