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

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

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