Given the position function, s of t equals t cubed divided by 3 minus 12 times t squared divided by 2 plus 36 times t , between t = 0 and t = 15, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right. (5 points) 0 < t < 6 5 < t < 15 t > 15 the particle always moves to the right.

Option D is correct.

as the particle always moves to the right

Step-by-step explanation:

Given the function:   , 0<t<15;

where

s(t) represent the distance in feet.

t represents the time in second.

Since, when the particle is moving to the right,

⇒ s(t) is increasing.

so,

Find the derivative of s(t) with respect to t;

Use derivative formula:

Simplify:

As

⇒

              [ ]

⇒ this is always true because square of any number is always positive

Therefore, it means that the particle always moves to the right.

12.5 feet

step-by-step explanation: