Q. The coordinates of a moving particle at any time $'t'$ are given by $x = \alpha t^{3}$ and $y = \beta t^{3}$. The speed of the particle at time $'t'$ is given by
A) $\sqrt{\alpha^{2} + \beta^{2}}$
B) $3t\sqrt{\alpha^{2} + \beta^{2}}$
C) $3t^{2}\sqrt{\alpha^{2} + \beta^{2}}$
D) $t^{2}\sqrt{\alpha^{2} + \beta^{2}}$
Explanation
(c) $x = \alpha t^{3}$ and $y = \beta t^{3}$ [Given]
$v_{x} = \frac{dx}{dt} = 3\alpha t^{2}$ and $v_{y} = \frac{dy}{dt} = 3\beta t^{2}$
Resultant velocity $= v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 3t^{2}\sqrt{\alpha^{2} + \beta^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.