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The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds. s(t)=3t^2−21t, t≥0 Find the velocity and acceleration functions. Over what interval is the particle moving in the positive direction?  Over what interval is the particle moving in the negative direction? Over what interval is the particle speeding up? Slowing down?

Hi, can you please show me the work and final answer to this problem?Thank you!

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The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds.s(t)=3t^2−21t, t≥0Find the velocity and acceleration functions.Over what interval is the particle moving in the positive direction? Over what interval is the particle moving in the negative direction?Over what interval is the particle speeding up? Slowing down?

To Determine:
The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds.
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/2c01f9e5-79e7-424f-851c-66ce5446a74b/82af2760-b300-4770-8b36-6518596c8b0d/cmsxs49.png" alt="Calculus homework question answer, step 1, image 1" />

Explanation:
Find the velocity and acceleration functions.
To find the velocity of the given speed function, we will find the first derivative with respect to t (time) of the speed function.
And take the derivative again for the acceleration.
Firstly find the velocity 
                             <img src="https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/2c01f9e5-79e7-424f-851c-66ce5446a74b/82af2760-b300-4770-8b36-6518596c8b0d/yx3fpgh.png" alt="Calculus homework question answer, step 2, image 1" />
Let's find the acceleration.
                          &amp;nb...

Calculus

Math

The function s(t) describes the position of a particle moving along a coordinate line, where s is in feet and t is in seconds.
<div>s(t)=3t^2−21t, t≥0</div>
Find the velocity and acceleration functions.
Over what interval is the particle moving in the positive direction? 
Over what interval is the particle moving in the negative direction?
Over what interval is the particle speeding up? Slowing down?

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