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

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Answer 1 · 2018-04-05T05:13:16

The speed is #=2.52ms^-1#

The speed is the derivative of the position

#p(t)=2t-cos(pi/6t)#

#v(t)=p'(t)=2+pi/6sin(pi/6t)#

And when #t=3#

#v(3)=2+pi/6sin(pi/6*3)#

#=2+pi/6sin(pi/2)#

#=2+pi/6#

#=2.52ms^-1#