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

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Answer 1 · 2017-06-08T04:32:47

The speed is #=3#

The speed is the derivative of the position

#p(t)=sin(3t-1/4pi)+3#

#v(t)=3cos(3t-1/4pi)#

When #t=3/4pi#, we have

#v(3/4pi)=3cos(3*3/4pi-1/4pi)#

#=3cos(9/4pi-1/4pi)#

#=3cos(8/4pi)#

#=3cos(2pi)#

#=3*1#

#=3#