The position of an object moving along a line is given by #p(t) = cos(t- pi /3) +1 #. What is the speed of the object at #t = (2pi) /3 #?

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Answer 1 · 2018-03-16T16:38:22

The speed is #=-sqrt3/2ms^-1#

The speed is the derivative of the position

#p(t)=cos(t-pi/3)+1#

#v(t)=p'(t)=-sin(t-pi/3)#

When #t=2/3pi#

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

#=-sin(1/3pi)#

#=-sqrt3/2ms^-1#