A particle starts from rest at the origin at time and moves along a line with…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle starts from rest at the origin at time

t=0\text{ s}

and moves along a line with acceleration

a(t)=\begin{cases} 4, & 0\le t\le 3,\\ -2, & 3< t\le 7, \end{cases}

where

a(t)

is measured in meters per second squared. What is the particle's displacement from the origin at

t=7\text{ s}

? (a)

32\text{ m}

(b)

50\text{ m}

(c)

66\text{ m}

(d)

26\text{ m}