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 at^(2)` and `v_(y) = (dy)/(dt) = 3 beta t^(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) )`