• anonymous
Let s=30/(t^2+12) be the position function of a particle moving along a coordinate line, where s is in feet and t is in seconds. (a) Find the maximum speed of the particle for t>=0 . If appropriate, leave your answer in radical form. Speed (ft/sec): ? (b) Find the direction of the particle when it has its maximum speed.
  • Stacey Warren - Expert
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
  • schrodinger
I got my questions answered at in under 10 minutes. Go to now for free help!
  • anonymous
part a) take the derivative of s with respect to "t" and then set it equal to zero to find the min and max points-(thats where the slope is zero or constant). speed = the absolute value of velocity which is what your finding in part a- velocity= change of position/ change of time take your value of time that you find in part a and plug it into your derivative equation to find the speed at the particle's max/min. part b) use your derivative in part a to tell whether the function is increasing or decreasing. If the function is decreasing, your velocity is slowing down; if the function is increasing your velocity is speeding up-so your either going one way or the other on your coordinate line. hope this helps you.

Looking for something else?

Not the answer you are looking for? Search for more explanations.