The position of an object moving along a line is given by #p(t) = t-cos(( pi )/4t) #. What is the speed of the object at #t = 7 #?

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Answer 1 · 2017-11-19T13:05:49

The speed is #=0.44ms^-1#

The speed is the derivative of the position

#p(t)=t-cos(1/4pit)#

#v(t)=p'(t)=1+1/4pisin(1/4pit)#

Therefore,

When #t=7s#

#v(7)=1+1/4pisin(1/4pixx7)=1+1/4pisin(7/4pi)#

#=0.44ms^-1#