Given position vectors of three points $\vec{P_1}, \vec{P_2} \& \vec{P_3}$ as function of time $(t)$
$$\vec{P_m} = p_{mx}(t) \hat{i} + p_{my}(t) \hat{j} : m \in \{1,2,3\}$$
These three points are located at the vertices of an equilateral triangle whose side equals $a$. They all start moving simulataneously the velocity $v$ constant in modulus, with first point heading continually for the second, the second for the third, and the third for the first. Initial positions for the points first lies at $(-\frac{a}{2},0)$, second at $(\frac{a}{2},0)$, and third at $(0,\sqrt{3}\frac{a}{2})$
- Find the scalar function $p_{mx}(t)$ and $p_{my}(t)$ $\forall{m} \in {1,2,3}$
- All three velocity vectors as a function of time.
- Find all three scalar functions, $ \widehat{acceleration}_{m}(t)\cdot\widehat{velocity}_{m}(t)$, as a function of time.