The position of an object moving along a line is given by #p(t) = 5t - cos(( pi )/3t) + 2 #. What is the speed of the object at #t = 13 #?

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Answer 1 · 2018-05-31T21:25:56

#v(13) = 5+ pi/(2 sqrt(3)) " distance per unit time"#

or

#v(13) = 5.9 " distance per unit time"#

The position function is given as

#p(t) = 5t - cos(pi/3 t) + 2#

We differentiate to obtain a velocity function

#v(t) = 5 + pi/3 sin(pi/3 t)#

Substitute #t=13# to find the speed at this time

#v(13) = 5+pi/3 sin(pi/3 (13))#

which can be simplified to

#v(13) = 5+ pi/(2 sqrt(3)) " distance per unit time"#

or

#v(13) = 5.9 " distance per unit time"#