APFIVE Vector Valued Function Acceleration
The position of a particle moving in the $$xy$$-plane is given by the vector $$\left\langle 4t^3, y(2t) \right\rangle$$, where $$y$$ is a twice-differentiable function of $$t$$. At time $$t = \dfrac{1}{2}$$, what is the acceleration vector of the particle?
A
$$\displaystyle \left\langle 12, 2y''(1) \right\rangle$$
B
$$\displaystyle \left\langle 6, 4y''(1) \right\rangle$$
C
$$\displaystyle \left\langle 3, 2y''(1) \right\rangle$$
D
$$\displaystyle \left\langle 12, 4y''(1) \right\rangle$$
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