Question

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

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

Answer 1

Answer: (B)

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

Answer 2

Speed $=\left|\vec{v}\right|=\sqrt{\left(3\alpha t^{2}\right)^{2}+\left(3\beta t^{2}\right)^{2}}=3t^{2}\sqrt{\alpha^{2}+\beta^{2}}.$