A particle moves with $x=15t^2$ and $y=10t^3$ for $0\le t\le 1$. Find the EXACT distance traveled.

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

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

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

A student writes the length of the path $x=3t$, $y=t^4$ on $\left[0,2\right]$ as ${\int }_0^2\sqrt{16t^6+9t^2}dt$. What is wrong with it?

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

A student writes the length of the path $x=4t$, $y=t^3$ on $\left[0,1\right]$ as ${\int }_0^1\sqrt{9t^4+16t^2}dt$. What is wrong with it?

Which integral gives the DISTANCE traveled by a particle with $x=2t^2-1$ and $y=t^3-4t$ for $0\le t\le 2$?

A particle has $x=6\cos t$ and $y=6\sin t$ for $0\le t\le 4\pi$, with $t$ in radians. What is the distance traveled, and what is the displacement?

A particle moves with $x=21t^2$ and $y=14t^3$ for $0\le t\le 1$. Find the EXACT distance traveled.

A particle has $x=\cos t$ and $y=\sin t$ for $0\le t\le \pi$, with $t$ in radians. What is the distance traveled, and what is the displacement?

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

A particle moves with $x=12t^2$ and $y=8t^3$ for $0\le t\le 1$. Find the EXACT distance traveled.

A particle has $x=\cos t$ and $y=\sin t$ for $0\le t\le 4\pi$, with $t$ in radians. What is the distance traveled, and what is the displacement?

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

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

Which integral gives the DISTANCE traveled by a particle with $x=4t$ and $y=2t^3$ for $0\le t\le 3$?

A particle moves with $x=3t^2$ and $y=3t^2+1$. What is its SPEED at $t=4$?

A particle moves with $x=9t^2$ and $y=6t^3$ for $0\le t\le 1$. Find the EXACT distance traveled.

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