For , a particle moves along a line so that its velocity, in meters per second, is .…

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

Problem

For

t\ge 0

, a particle moves along a line so that its velocity, in meters per second, is

v(t)=e^{0.5t}-t

. At time

t=2

seconds, the particle is located 7 meters to the right of the origin, so that

s(2)=7

. Let

s(t)

denote the particle’s position (in meters) at time

t

. (a) Determine an explicit formula for

s(t)

valid for

t\ge 0

. (b) Find

s(0)

and interpret its meaning in the context of the motion. (c) Determine the average velocity of the particle on the interval

0\le t\le 2

. Express your answer in exact form.