CARRIE AND HER DOT BANNER ARE DRIVIVNG IN A STRIGHT LINE FROM CITY A TO CITY B.T

Question

CARRIE AND HER DOT BANNER ARE DRIVIVNG IN A STRIGHT LINE FROM CITY A TO CITY B.THEY LEAVE CITY A AT 8:00 AM AND THEIR TRIP CAN BE DEXCRIBED BY THE POSITION FUNCTION(GIVEN IN MILES): S(t) = 12t3 - 90t2 + 216t AND T IS TIME IN HOVES. WHAT IS HER VELOCITY AT 9:00 AM? AT SOME POINT DURING THE TRIP, CARRIE TURNS AROUND AND DRIVES BACK TOWARDS CITY 'A'.BEFORE SHE TETS TO CITY 'A' SHE TURNS BACK AROUND AND RESUMES HER TRIP TO CITY 'B'. AT WHAT TIME DOES SHE TURN AROUND (CHANCE DIRCETION) FOR THE 1ST TIME?FOR THE 2ND TIME? HOW MANY MILES DOES SH BACKTRACK BEFORE TURNING AROUND AND RESUMING HER TRIP?

Explanation / Answer

s=12t^3-90t^2+216t v=36t^2-180t+216 for t=1,v=72miles/hr. v=0 at t=2 hr and t=3 hr for calculating the distance, s(2) and s(3) must be known s(2)-s(3)=6 miles

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