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/3 #?

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Answer 1 · 2017-07-17T12:04:55

The speed is #=(sqrt6-sqrt2)/2=0.52#

The speed is the derivative of the position

#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#