During a six-hour interval

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

During a six-hour interval, a space probe moves directly away from a planet. For

0\le t\le 6

(hours), its velocity (in kilometers per second) is modeled by

v(t)=c\,\sin\!\left(\frac{\pi t}{6}\right),

where

c

is a positive constant. (a) Express the probe’s average velocity on

0\le t\le 6

in terms of

c

. Write your answer as an exact value. (b) The average velocity during this interval is measured to be

1.2\text{ km/s}

. Determine the value of

c

to the nearest hundredth. (c) Using the value of

c

found in part (b), find the maximum distance (to the nearest kilometer) the probe is from its starting position during the six-hour interval. Indicate the time at which this maximum distance occurs.

Related theory

Applications of Integration

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