The co-ordinates of moving particle at any time t are given by x = `at^(2)` and y = b`t^(2)`. The velocity magnitude of the particle :

Options

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

Answer

D

Explanation

`V_(x)=dx/dt=2at`
`V_(y)=(dy)/(dt)=2bt`
`:. V=sqrt(V_(x)^(2) + V_(y)^(2))=sqrt(4a^(2)t^(2) + 4b^(2)t^(2))`
`=2tsqrt(a^(2)+ b^(2))`