Question

A particle starts from origin at t = 0 and moves in the xy plane with a constant acceleration α in the y – direction. The equation of motion is y = kx². Its velocity component along x – direction is

• A. Variable
• B. $\sqrt{2\alpha/k}$
• C. $\alpha/2k$
• D. $\sqrt{\alpha/2k}$

Answer 1

Answer: (D)

$\sqrt{\alpha/2k}$

Answer 2

y = kx² or $\frac{dy}{dt} = 2kx\frac{dx}{dt}$

and $\frac{d^{2}y}{dt^{2}} = 2k\left( \frac{dx}{dt} \right)^{2} + 2kx\frac{d^{2}x}{dt^{2}}$.

$\frac{d^{2}x}{dt^{2}}$ = 0 ∴ $\frac{dx}{dt}$ = $\sqrt{\frac{\alpha}{2k}}$