problem 3: a remote control boat has an acceleration of a = (4,1) m/s². given that the boat starts from…

Explanation:

Step1: Recall the displacement - time formula for constant acceleration

The formula for displacement $\vec{s}$ of an object with constant acceleration $\vec{a}$ starting from rest ($\vec{u} = 0$) is $\vec{s}=\vec{u}t+\frac{1}{2}\vec{a}t^{2}$. Since $\vec{u} = 0$, the formula simplifies to $\vec{s}=\frac{1}{2}\vec{a}t^{2}$.

Step2: Substitute the given values

We are given $\vec{a}=(4,1)\ m/s^{2}$ and $t = 2.3\ s$. First, calculate $t^{2}=(2.3)^{2}=5.29$. Then, $\frac{1}{2}t^{2}=\frac{1}{2}\times5.29 = 2.645$. Multiply each component of the acceleration vector by $\frac{1}{2}t^{2}$. For the $x$ - component: $s_{x}=\frac{1}{2}a_{x}t^{2}=2.645\times4 = 10.58\ m$. For the $y$ - component: $s_{y}=\frac{1}{2}a_{y}t^{2}=2.645\times1 = 2.645\ m$. So the displacement vector $\vec{s}=(10.58,2.645)\ m$.

Answer:

$(10.58,2.645)\ m$