The coordinates of a moving particle at any time ‘t’ are given by x = αt3 and y = βt3. The speed of the particle at time ‘t’ is given by

(1) $\sqrt{{\alpha }^{2}+{\beta }^{2}}$

(2) $3\text{\hspace{0.17em}}t\sqrt{{\alpha }^{2}+{\beta }^{2}}$

(3) $3\text{\hspace{0.17em}}{t}^{2}\sqrt{{\alpha }^{2}+{\beta }^{2}}$

(4) ${t}^{2}\sqrt{{\alpha }^{2}+{\beta }^{2}}$

Concept Videos :-

#3 -Instantaneous-Velocity--Speed
#4-Solved-Examples-1
#5-Solved-Examples-4

Concept Questions :-

Speed and velocity

(3) $x=\alpha {t}^{3}$ 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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