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

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Answer 1 · 2016-04-09T09:48:16

Speed #p' (3)=2#

Given the position equation #p(t)=2t-sin((pit)/6)#
The speed is the rate of change of the position p(t) with respect to t.

We calculate the first derivative at t=3

#p' (t)=d/dt(2t-sin((pit)/6))#

#p' (t)=d/dt(2t)-d/dt sin((pit)/6)#

#p' (t)=2-(pi/6)*cos((pit)/6)#

at #t=3#
#p' (3)=2-(pi/6)*cos((pi*3)/6)#

#p' (3)=2-0#

#p' (3)=2#

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