The coordinates of a body moving in a plane at any instant of time t are `x=alphat^(2)` and `y=betat^(2)`. The velocity of the body is

Explanation

`x=alphat^(2) rArr v_(x) =(dx)/(dt) =2alphat`
`y=betat^(2), rArr v_(y) =(dy)/(dt) =2betat`
`therefore` velocity `v=sqrt(v_(x)^(2) + v_(y)^(2)) rArr sqrt((2alphat)^(2) + (2betat)^(2))`
`=2tsqrt(alpha^(2) + beta^(2))`