A car’s speed (in miles per hour) was measured at noon and again five minutes later

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A car’s speed

v(t)

(in miles per hour) was measured at noon and again five minutes later. The data show

v(12{:}00)=40

and

v(12{:}05)=55

. It is known that

v(t)

may have an instantaneous jump in value at 12{:}03. Which of the following conclusions is necessarily true? (a) The speed was exactly

50\text{ mph}

at some time between

12{:}00

and

12{:}05

. (b) No conclusion can be drawn about a time when the speed was exactly

50\text{ mph}

, because continuity is not assured. (c) Because the average speed over the interval is

47.5\text{ mph}

, the car must have been traveling exactly

47.5\text{ mph}

at some instant during the five minutes. (d) The speed was increasing throughout the entire five-minute interval.