At an instasnt `t` the coordinates of a particles are `x=at^(2), y=bt^(2)` and `z=-0`. The magnitude of velocity of particle at an instant is

Options

A. `tsqrt(a^(2)+b^(2))`
B. `2tsqrt(a^(2)+b^(2))`
C. `sqrt(a^(2)+b^(2))`
D. `2t^(2)sqrt(a^(2)+b^(2))`

Answer

B

Explanation

`{:(x=at^(2),y=bt^(2),z=0),((dx)/(dt)=2at,(dy)/(dt)=2bt,V_(x)=0):}`
`V_(x)=2atV_(y)=2bt`
`V=sqrt(V_(x)^(2)+V_(y)^(2)+V_(z)^(2))`
`V=2tsqrt(a^(2)+b^(2))`