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= beta t^(2) rArr v_(y)=(dy)/(dt)=2betya`
`:. velocity v= sqrt(v_(x)^(2)+v_(y)^(2)) rArr sqrt((2 alpha t)^(2)+( 2 beta t)^(2))`
`=2t sqrt(alpha^(2)+beta^(2))`