The co-ordinates of a moving particle at anytime '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. `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

B

Explanation

`x= alpha t^(3) and y = beta t^(3)`
`v_(x) = (dx)/(dt) = 3 alpha t^(2) and v_(y) = (dy)/(dt) = 3 beta^(2)`
`:. v= sqrt(v_(x)^(2) + v_(y)^(2))= sqrt(9 alpha^(2) t^(4) + 9 beta^(2) t^(4)) = 3 t^(2) sqrt(alpha^(2) + beta^(2))`