The position of an object moving along a line is given by #p(t) = sin(t- pi /2) +3 #. What is the speed of the object at #t = pi/6 #?

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Answer 1 · 2017-12-09T09:34:12

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

The position of the object is

#p(t)=sin(t-pi/2)+3=-cos(t)+3#

The speed is the derivative of the position

#v(t)=p'(t)=sint#

Therefore,

When #t=pi/6#

The speed is

#v(pi/6)=sin(pi/6)=1/2#