Question

A particle moves along a parabolic path $y = 9x^2$ in such a way that the x-component of velocity remains constant. If the total acceleration of the particle is $2\hat{j}\text{ m s}^{-2}$, find the x-component of velocity.

• A. $\frac{1}{9}\text{ m s}^{-1}$
• B. $\frac{1}{3}\text{ m s}^{-1}$
• C. $\frac{1}{4}\text{ m s}^{-1}$
• D. $\frac{1}{6}\text{ m s}^{-1}$

Hint:

For any path of the form $y = kx^2$ where $v_x$ is constant, the vertical acceleration component simplifies perfectly to $a_y = 2k\cdot v_x^2$. Memorizing this short form helps solve calculus-based kinematics problems quickly.

Answer 1

The Correct Option is B