The coordinates of a moving particle at time t are given by `x=ct^(2)` and `y=bt^(2)`. The speed of the particle is given by :-

Options

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

Answer

D

Explanation

`(dx)/(dt) = 2 c t and (dy)/(dt) =2 b t`
`: v= sqrt({((dx)/(dt))^(2) + ((dy)/(dt))^(2)})`
`= sqrt({(2ct)^(2) + (2bt)^(2)}) = 2t sqrt((c^(2) + b^(2)))`