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

Answer

C

Explanation

`x = alpha t^(3) rArr v_(x) = (d x)/(d t) = 3 beta t^(2)`
`y = beta t^(3) rArr v_(y) = (d y)/(d t) = 3 beta t^(2)`
`v = sqrt(v_(x)^(2) + v_(y)^(2)) = 3 t^(2) sqrt(alpha^(2) + beta^(2))`