<p>A particle travels with the position function s(t) = 3t^3 -t where distance is measured in feet and time is measured in seconds. What is the average velocity of the particle at time [1,3]?</p>
<p>44 ft/s
40 ft/s
36 ft/s
18 ft/s ??</p>
<p>These were the only three choices I remember from my exam. The fourth choice might be on it too, but I'm not quite sure.</p>
<p>(position2 - position1)/(time2 - time1)</p>
<p>s'(t)=9t^2-1</p>
<p>jenkster gives you average velocity and indianbasketball gives you instantaneous velocity</p>
<p>...so the answer is 38 ft/s. That was not one of the choices. I hope the teacher doesn't count that question.</p>
<p>The biggest problem with the instantaneous velocity here is that you can't find an instantaneous velocity over an interval anyway...</p>
<p>Yes, the answer is 38 ft/s. Calculus is not needed to find the average velocity in this situation (only needed for instantaneous velocity).</p>
<p>Yep my bad its average v.</p>
<p>I wonder if the problem intended for (v2 + v1)/2 to be the solution. However, the acceleration obviously isn't constant and you can't use the above formula if the acceleration isn't constat. Oh well. you can argue w/ your teacher.</p>