The position of an object moving along a line is given by #p(t) = sin(t- pi /4) +1 #. What is the speed of the object at #t = pi/3 #?

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Answer 1 · 2017-05-02T21:07:55

The speed is #=0.97ms^-1#

The speed is the derivative of the position.

#p(t)=sin(t-pi/4)+1#

#v(t)=p'(t)=cos(t-pi/4)#

Therefore,

when #t=pi/3#

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

#=cos(pi/12)#

#=0.97ms^-1#