a-rescue-craft-moves-so-that-at-6t-2i-4t3j-with-v0-3i-5j-and-r0-2i-what-is-rt

Question

A rescue craft moves so that a→(t)=(6t−2)i^+(4t3)j^\overrightarrow{a}\left(t)\right.=\left(6t-2\right)\hat{i}+\$$left(4t^3$$\right)\hat{j}, with v→(0)=−3i^+5j^\overrightarrow{v}\left(0\right)=-3\hat{i}+5\hat{j} and r→(0)=2i^\overrightarrow{r}\left(0\right)=2\hat{i}. What is r→(t)\overrightarrow{r}\left(t\right)?

Accepted Answer

(t3−t2−3t+2)i^+(t55+5t)j^\$$left(t^3$-t^2-3t+2$$\right)\hat{i}+\left(\frac{$$t^5$$}{5}+5t\right)\hat{j}

Answer

(3t2−2t−3)i^+(t4+5)j^\$$left(3t^2-2t-3$$\right)\hat{i}+\$$left(t^4+5$$\right)\hat{j}

Answer

(t2−t2−3t)i^+(t55+5t)j^\$$left(t^2$-t^2-3t$$\right)\hat{i}+\left(\frac{$$t^5$$}{5}+5t\right)\hat{j}

Answer

(t3−t2−3t+2)i^+(t55+5t+2)j^\$$left(t^3$-t^2-3t+2$$\right)\hat{i}+\left(\frac{$$t^5$$}{5}+5t+2\right)\hat{j}