The position of an object moving along a line is given by $p (t) = sin (2 t - \frac{π}{4}) + 2$ $p(t) = sin(2t- pi /4) +2$ . What is the speed of the object at $t = \frac{π}{3}$ $t = pi/3$ ?

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Answer 1 · 2017-07-17T12:04:55

The speed is $= \frac{\sqrt{6} - \sqrt{2}}{2} = 0.52$ $=(sqrt6-sqrt2)/2=0.52$

The speed is the derivative of the position

$p (t) = sin (2 t - \frac{π}{4}) + 2$ $p(t)=sin(2t-pi/4)+2$

$v(t)=p'(t)=2cos(2t-pi/4)$

When $t=pi/3$

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

$=2cos(2/3pi-1/4pi)$

$=2*(cos(2/3pi)*cos(pi/4)+sin(2/3pi)*sin(1/4pi))$

$=2*(-1/2*sqrt2/2+sqrt3/2*sqrt2/2)$

$=(sqrt6-sqrt2)/2=0.52$

The position of an object moving along a line is given by p(t) = sin(2t- pi /4) +2 p(t)=sin(2t−π4)+2p(t) = sin(2t- pi /4) +2 . What is the speed of the object at t = pi/3 t=π3t = pi/3 ?