For a particle moving along a line

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

Problem

For a particle moving along a line, its velocity

v(t)

(in m/s) satisfies

v(t)<0

for

0<t<1

v(t)>0

for

1<t<3

, and

v(t)<0

for

t>3

, with

v(t)=0

only at

t=1

and

t=3

. Which statement about the particle’s motion is correct? (a) The particle changes direction only at

t=3\,\text{s}

; at

t=1\,\text{s}

it briefly pauses while still heading left. (b) The particle is at rest at both

t=1\,\text{s}

and

t=3\,\text{s}

but does not reverse direction at either instant. (c) The particle changes direction at both

t=1

s and

t=3

s. (d) The particle changes direction only at

t=1\,\text{s}

; at

t=3\,\text{s}

it stops but continues to move to the right afterward.