A particle starts from the origin of coordinates at time 𝑡 = 0 and moves in the 𝑥 − 𝑦 plane with a constant acceleration α in the 𝑦-diretion. Its equation of motion is 𝑦 = β𝑥 2 . Its velocity component in the 𝑥- direction is

Question: A particle starts from the origin of coordinates at time 𝑡 = 0 and moves in the 𝑥 − 𝑦 plane with a constant acceleration α in the 𝑦-diretion. Its equation of motion is 𝑦 = β𝑥 2 . Its velocity component in the 𝑥- direction is

(A) Variable

(B) $\sqrt{\dfrac{2a}{\beta }}$

(C) $\dfrac{a}{2\beta }$

(D) $\sqrt{\dfrac{a}{2\beta }}$