Water enters a tank at a rate of $r(t)=6t-t^2$ gallons per hour, for $0\le t\le 4$. What is the total change over those $4$ hours?

A particle is at position $s(0)=2$ meters and has velocity $v(t)=9t^2$ meters per second. Find its position at $t=4$.

A particle moves along a line with velocity $v(t)=t^2-5t$ meters per second, for $0\le t\le 9$. Find the particle's DISPLACEMENT over that interval.

A particle moves along a line with velocity $v(t)=t^2-2t$ meters per second, for $0\le t\le 6$. Find the particle's DISPLACEMENT over that interval.

A particle is at position $s(0)=8$ meters and has velocity $v(t)=15t^2$ meters per second. Find its position at $t=1$.

The graph shows the velocity $v(t)=t^2-3t$, in meters per second, of a particle moving along a line for $0\le t\le 6$. Find the TOTAL DISTANCE it travels over that interval.

The graph shows a particle's velocity $v(t)$ on $\left[0,9\right]$. Which expression gives the DISPLACEMENT of the particle on $\left[0,9\right]$?

Oil leaks from a drum at a rate of $L(t)=5t-t^2$ liters per minute, for $0\le t\le 1$. How much oil leaks out over that $1$ minute?

Oil leaks from a drum at a rate of $L(t)=7t-t^2$ liters per minute, for $0\le t\le 4$. How much oil leaks out over those $4$ minutes?

The graph shows the velocity $v(t)=t^2-2t$, in meters per second, of a particle moving along a line for $0\le t\le 4$. Find the TOTAL DISTANCE it travels over that interval.

A particle is at position $s(0)=-2$ meters and has velocity $v(t)=18t^2$ meters per second. Find its position at $t=3$.

The graph shows the velocity $v(t)=t^2-5t$, in meters per second, of a particle moving along a line for $0\le t\le 9$. Find the TOTAL DISTANCE it travels over that interval.

The graph shows the velocity $v(t)=t^2-6t$, in meters per second, of a particle moving along a line for $0\le t\le 8$. Find the particle's DISPLACEMENT over that interval.

Water enters a tank at a rate of $r(t)=3t-t^2$ gallons per hour, for $0\le t\le 2$. What is the total change over those $2$ hours?

The graph shows the velocity $v(t)=t^2-4t$, in meters per second, of a particle moving along a line for $0\le t\le 8$. Find the TOTAL DISTANCE it travels over that interval.

The graph shows the velocity $v(t)=t^2-4t$, in meters per second, of a particle moving along a line for $0\le t\le 7$. Find the particle's DISPLACEMENT over that interval.

A particle's velocity $v(t)$ changes sign twice on $\left[0,12\right]$, and its position at $t=0$ is $s(0)$. Which expression gives its POSITION at $t=12$?

The graph shows the velocity $v(t)=t^2-5t$, in meters per second, of a particle moving along a line for $0\le t\le 7$. Find the particle's DISPLACEMENT over that interval.

The graph shows the velocity $v(t)=t^2-2t$, in meters per second, of a particle moving along a line for $0\le t\le 6$. Find the TOTAL DISTANCE it travels over that interval.

The graph shows a particle's velocity $v(t)$ on $\left[0,6\right]$. Which expression gives the TOTAL DISTANCE the particle travels on $\left[0,6\right]$?

A particle is at position $s(0)=-3$ meters and has velocity $v(t)=15t^2$ meters per second. Find its position at $t=3$.

A drum starts with $50$ liters of oil. Oil leaks out at a rate of $L(t)=6t-t^2$ liters per minute, for $0\le t\le 4$. How much oil is in the drum at $t=4$?

The amount of water in a tank changes at a rate of $r(t)=4t-t^2$ liters per minute, for $0\le t\le 5$. What is the net change in the amount of water over those $5$ minutes?

The graph shows the velocity $v(t)=t^2-3t$, in meters per second, of a particle moving along a line for $0\le t\le 7$. Find the TOTAL DISTANCE it travels over that interval.