Let be the velocity (in meters per second) of a particle for seconds

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

v(t)=e^{-t}

be the velocity (in meters per second) of a particle for

0\le t\le2

seconds. At which of the following times

t=c

does the particle’s instantaneous velocity equal its average velocity on

[0,2]

? (a)

c\approx0.57\text{ s}

(b)

c\approx1.00\text{ s}

(c)

c\approx0.84\text{ s}

(d)

c\approx0.69\text{ s}