The co-ordinates of a moving particle at any time ' t ' are given by $x=\alpha \mathrm{t}^3$ and $y=\beta \mathrm{t}^3$ where $\alpha$ and $\beta$ are constants. The speed of the particle at time ' $t$ ' is given by

Question

Aicharya · Accepted Answer

$\begin{aligned} & X=\alpha t^3 \hat{i}+\beta t^3 \hat{j} \ & \begin{aligned} V=\frac{d X}{d t}=3 \alpha t^2 \hat{i} & +3 \beta t^2 \hat{j} \ 	ext { Magnitude of } V & =\sqrt{\left(3 \alpha t^2ight)^2+\left(3 \beta t^2ight)^2} \ & =\sqrt{9 \alpha^2 t^4+9 \beta^2 t^4} \ & =\sqrt{9 t^4\left(\alpha^2+\beta^2ight)} \ & =3 t^2 \sqrt{\alpha^2+\beta^2}\end{aligned}\end{aligned}$

The co-ordinates of a moving particle at any time ' t ' are given by $x=\alpha \mathrm{t}^3$ and $y=\beta…

Solution