The position of an object moving along a line is given by $p(t) = sin(2t- pi /4) +2$ . What is the speed of the object at $t = pi/2$ ?

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Answer 1 · 2016-04-29T09:01:09

$v(pi/2)=-sqrt2$

$if p=f(t);$

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

$v=d/(d t) (sin(2t-pi/4)+2)$

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

$"for :"t=pi/2$

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

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

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

$cos( (3pi)/4)=-cos (pi/4)=-sqrt2/2$

$v(pi/2)=-2*sqrt2/2$

$v(pi/2)=-sqrt2$

The position of an object moving along a line is given by p(t) = sin(2t- pi /4) +2 p(t) = sin(2t- pi /4) +2 . What is the speed of the object at t = pi/2 t = pi/2 ?