A particle moves with $x=t^3$ and $y=t^2-t$. What is its SPEED at $t=1$?

The graph shows the curve $r=6\left(1+\sin \theta \right)$. Which integral gives the area it encloses?

A particle moves with $x=t^2+t$ and $y=t^3-3t$. What is its SPEED at $t=4$?

A particle has position $r(t)=⟨e^{2t},t^2-3t⟩$. Find its VELOCITY vector.

A curve is given by $x=t^2$ and $y=t^3-4t$. Find $\frac{dy}{dx}$.

A particle has velocity $v(t)=⟨3t^2,6t⟩$. Find its ACCELERATION at $t=2$.

Find $\frac{dy}{dx}$ for $r=6\sin \theta$ at $\theta =\frac{\pi }{3}$, with $\theta$ in radians.

A particle has velocity $v(t)=⟨3t^2,8t⟩$. Find its ACCELERATION at $t=1$.

Which integral gives the DISTANCE traveled by a particle with $x=2t^2-1$ and $y=t^3$ for $0\le t\le 2$?

Find $\frac{dy}{dx}$ for $r=5\sin \theta$ at $\theta =\frac{\pi }{4}$, with $\theta$ in radians.

For $x=2t+1$ and $y=t^2-t$, find $\frac{dy}{dx}$ at $t=1$.

A particle moves with $x=t^2+t$ and $y=2t^3$. What is its SPEED at $t=2$?

A curve is given by $x=t^2+1$ and $y=3t^2+1$. Find $\frac{dy}{dx}$.

Which integral gives the DISTANCE traveled by a particle with $x=t+2$ and $y=t^3-3t$ for $0\le t\le 3$?

For $x=2t^2-1$ and $y=t^4$, find $\frac{dy}{dx}$ at $t=2$.

The graph shows the curve $r=5\sin \theta$. Which integral gives the area it encloses?

The graph shows the curve $r=8\sin \theta$. Which integral gives the area it encloses?

A particle has position $r(t)=⟨\sin t,2t^3⟩$. Find its VELOCITY vector.

Find $\frac{dy}{dx}$ for $r=4\cos \theta$ at $\theta =\frac{\pi }{2}$, with $\theta$ in radians.

A particle has velocity $v(t)=⟨9t^2,2t⟩$. Find its ACCELERATION at $t=2$.

A particle has position $r(t)=⟨\sin t,\cos t⟩$. Find its VELOCITY vector.

For $x=3t^2$ and $y=t^3$, find $\frac{dy}{dx}$ at $t=-2$.

A curve is given by $x=t^3$ and $y=t^3-4t$. Find $\frac{dy}{dx}$.

A particle has velocity $v(t)=⟨6t^2,6t⟩$. Find its ACCELERATION at $t=1$.