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#