The position of an object moving along a line is given by #p(t) = 7t - cos(( pi )/3t) + 2 #. What is the speed of the object at #t = 5 #?

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Answer 1 · 2017-07-22T09:40:41

The speed is #=6.09ms^-1#

We need

#(cosx)'=-sinx#

The speed is the derivative of the position

#p(t)=7t-cos(pi/3t)+2#

#v(t)=p'(t)=7+1/3pisin(pi/3t)#

The speed at #t=5# is

#v(5)=7+1/3pisin(5/3pi)#

#=7+pi/3*-sqrt3/2#

#=6.09ms^-1#