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

1 Answer
Nathan L.
Jul 20, 2017

#v(5) = 1.09# #"LT"^-1#

Explanation:

We're asked to find the speed of an object at #t = 5# (no units) with a given position equation,

To do this, we need to find the object's velocity as a function of time, by differentiating the position equation:

#v = (dp)/(dt) = d/(dt) [2t - cos(pi/3t) + 2] = color(red)(2 + pi/3sin(pi/3t)#

Now all we have to do is plug in #5# for #t# to find the velocity at #t = 5#:

#v(5) = 2 + pi/3sin(pi/3(5)) = color(blue)(1.09# #color(blue)("LT"^-1#

(The #"LT"^-1# term is the dimensional form of velocity; I used it here merely because no units were given.)

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