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
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
$\sqrt {{\alpha ^2} + {\beta ^2}} $
$3\,t\sqrt {{\alpha ^2} + {\beta ^2}} $
$3\,{t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $
${t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $
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
$x = \alpha {t^3}$ 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} = 3{t^2}\sqrt {{\alpha ^2} + {\beta ^2}} $
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