A particle moves along a straight line with a velocity given by a continuous

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

Problem

A particle moves along a straight line with a velocity given by a continuous, non-negative function

v(t)

, measured in meters per second, for

0\le t\le 8

. Distance is measured in meters and time in seconds. (a) Explain the physical meaning, including units, of the quantity

\displaystyle \int_{0}^{8} v(t)\,dt

. Describe what information about the particle’s motion it conveys. (b) The particle is located at position

s=5\text{ m}

t=0

. Describe, in words and with a clear mathematical expression, how to determine the particle’s position at

t=8

. Explain why your expression is valid.