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

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Answer 1 · 2016-05-24T10:04:01

$"Speed of object is: "v((2pi)/3)=-1/2$

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

$v(t)=d/(d t) [cos(t-pi/2)]$

$v(t)=-sin(t-pi/2)$

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

$v(2pi/3)=-sin(pi/6)$

$sin (pi/6)=1/2$

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

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