Starting at time 𝑡=0 from the origin with speed 1 ms$$^{-1}$$, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation $$y = \frac{x^2}{2}$$. The x and y components of its acceleration are denoted by $$𝑎_𝑥$$ and $$𝑎_y$$, respectively. Then

A

$$a_x = 1$$ ms$$^{-2}$$ implies that when the particle is at the origin, $$a_y = 1$$ ms$$^{-2}$$

B

$$a_x = 0$$ implies $$a_y = 1$$ ms$$^{-2}$$ at all times

C

at 𝑡=0, the particle’s velocity points in the 𝑥-direction

D

$$a_x = 0$$ implies that at 𝑡 = 1 s, the angle between the particle’s velocity and the 𝑥 axis is $$45^\circ$$