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

Options

A. `sqrt(alpha^(2)+beta^(2))`
B. `3tsqrt(alpha^(2)+beta^(2))`
C. `3t^(2)sqrt(alpha^(2)+beta^(2))`
D. `t^(2)sqrt(alpha^(2)+beta^(2))`

Answer

C

Explanation

`V_(X)=(dx)/(dt),V_(y)=(dy)/(dt),v=sqrt(V_(X)^(2)+V_(y)^(2))`