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

1 Answer
May 10, 2016

Answer:

#v((2pi)/3)=-2#

Explanation:

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

#v(t)=d/(d t)(sin(2t-pi/3)+2)#

#v(t)=2*cos(2t-pi/3)#

#"for "t=((2pi)/3) rarr v((2pi)/3)=2*cos(2*(2pi)/3-pi/3)#

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

#v((2pi)/3)=2*cos pi#

#cos pi=-1#

#v((2pi)/3)=-2*1#

#v((2pi)/3)=-2#