Question

The coordinates of a moving particle at any time t are given by $x=a{t}^3$ and $y=b{t}^3$. The speed of the particle at time t is given by

• A. $t^2\sqrt{{\alpha }^2+{\beta }^2}$
• B. $3t^2\sqrt{{\alpha }^2+{\beta }^2}$
• C. $\sqrt{{\alpha }^2+{\beta }^2}$
• D. $3t\sqrt{{\alpha }^2+{\beta }^2}$

Answer 1

The correct option is B $3t^2\sqrt{{\alpha }^2+{\beta }^2}$

$x=\alpha t^3\Rightarrow v_x=\frac{dx}{dt}=3\alpha t^{2}y=\beta t^2\Rightarrow v_y=\frac{dy}{dt}=3\beta t^{2}v=\sqrt{v_x^2+v_y^2}=3t^2\sqrt{{\alpha }^2+{\beta }^2}$