$A$ particle is moving in the $xy$-plane such that its position coordinates are given by $x = (4t + t^2) \text{ m}$ and $y = (2t + \frac{t^2}{2}) \text{ m}$, where $t$ is in seconds. What is the velocity of the particle?

• A
  $\vec{v} = (4 + t) \hat{i} + (2 + t) \hat{j}$
• B
  $\vec{v} = (4 + 2t) \hat{i} + (2 + t) \hat{j}$
• C
  $\vec{v} = (4 + 2t) \hat{i} + (2 + \frac{t}{2}) \hat{j}$
• D
  $\vec{v} = (4 + t) \hat{i} + (2 + \frac{t}{2}) \hat{j}$