A particle moves along a straight line with velocity given

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle moves along a straight line with velocity given, for all

t\ge 0

(in seconds), by

v(t)=3t^{2}-4t+1

meters per second. The particle’s position is denoted by

s(t)

, measured in meters. Assume

s(0)=5

. (a) Determine an explicit expression for

s(t)

. (b) Calculate the particle’s displacement on the time interval

0\le t\le 3

. (c) Compute the total distance the particle travels on the interval

0\le t\le 3

, and explain how you arrived at your result by referencing the sign of the velocity function.