Answer
(a) $~~\int_{60}^{120}v(t)~dt~~$ is an object's net displacement between the times $60$ and $120$
(b) $~~\int_{60}^{120}\vert v(t) \vert~dt~~$ is the total distance covered by an object between the times $60$ and $120$
(c) $~~\int_{60}^{120}a(t)~dt~~$ is an object's net change in velocity between the times $60$ and $120$
Work Step by Step
$x(t)$ is an object's position at time $t$
$\frac{dx}{dt} = v(t)$ is an object's velocity at time $t$
$\frac{dv}{dt} = a(t)$ is an object's acceleration at time $t$
Note that $\Delta x$ is an object's change in position, which is called displacement.
(a) $~~\int_{60}^{120}v(t)~dt~~$ is an object's net displacement between the times $60$ and $120$
(b) $~~\int_{60}^{120}\vert v(t) \vert~dt~~$ is the total distance covered by an object between the times $60$ and $120$
(c) $~~\int_{60}^{120}a(t)~dt~~$ is an object's net change in velocity between the times $60$ and $120$
