An autonomous electric vehicle travels along a straight test track
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
An autonomous electric vehicle travels along a straight test track. The vehicle’s position from the starting line is modeled by the function s(t), where t represents elapsed time.
Engineers report that when the vehicle has traveled for t=90 seconds, its instantaneous velocity is s′(90)=88 ft/s.
The engineers would like to express the position function s using miles as the unit of distance and minutes as the unit of time.
(a) Determine the unit of s(t) that is consistent with the given information. Justify your answer by analyzing how the units of s and t combine to produce the units of s′(t). (No numerical conversion is necessary in this part.)
(b) Convert the recorded instantaneous velocity s′(90)=88 ft/s to units of miles per minute. Show all conversion factors symbolically before computing a numerical value.
(c) Using your result from part (b), write a complete sentence interpreting the value of s′(90) in the new unit system. Include both the numerical value and the appropriate units in your interpretation.