$R$, a closed, bounded, connected region in the plane, moves at a rate of 2 units per second in the direction of $4\vec{i}+3\vec{j}$. At time $t$ seconds, with $-\infty

Question

$R$, a closed, bounded, connected region in the plane, moves at a rate of 2 units per second in the direction of $4\vec{i}+3\vec{j}$. At time $t$ seconds, with $-\infty<t<\infty$, the area of the portion of $R$ between the lines $x=11$ and $x=15$ is given by the function...

anonymous · Answer

$$A(t)=\begin{cases}
0&\text{for }t<=5\\
-\dfrac{16}{25}t^2+\dfrac{124}{5}t-108&\text{for }5\le t\le\dfrac{15}{2}\\
-\dfrac{16}{5}t+66&\text{for }\dfrac{15}{2}\le t\le15\\
\dfrac{16}{25}t^2-28t+294&\text{for }15\le t\le\dfrac{35}{2}\\
0&\text{for }t\ge\dfrac{35}{2}
\end{cases}$$
Find the area of $R$.

jhannybean · Answer

Your alignment skills are impeccable.