Question

Solve this:

$$\begin{gathered} \mathit{Q}\mathbf{.}\mathbf{}\mathbf{}Atanins\tan tt,thecoordinatesofaparticlesarex=a{t}^2,y=b{t}^{2}andz=0.Themagnitudeofvelocityofparticleatanins\tan ttis \\ \mathit{a}\mathbf{.}t\sqrt{a^2+b^2}\mathbf{}\mathit{b}\mathbf{.}\frac{v}{\sqrt{2}}\mathbf{}\mathit{c}\mathbf{.}\frac{v}{\sqrt{3}}\mathit{d}\mathbf{.}2t\sqrt{a^2+b^2} \end{gathered}$$

Answer 1

Dear Student,
$$\begin{gathered} Here \\ {v}_x=\frac{dx}{dt}=2at \\ {v}_y=\frac{dy}{dt}=2bt \\ {v}_z=\frac{dz}{dt}=0 \\ hence \\ v=\sqrt{{v_x}^2+{v_y}^2+{v_z}^2}=\sqrt{{\left(2at\right)}^2+{\left(2bt\right)}^2+{\left(0\right)}^2}=2t\sqrt{a^2+b^2} \end{gathered}$$
Regards