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

Options

A. `2t sqrt(b^(2)-c^(2))`
B. `sqrt(4b^(2)t^(2)+c^(2))`
C. `2t(b+c)`
D. `2t(b-c)`

Answer

B

Explanation

Given, `x = ct rArr v_(x) = (dx)/(dt) = c`
Also, `y = bt^(2) rArr v_(y) = (dy)/(dt) = 2bt`
`:.` Speed `=|v| = sqrt(v_(x)^(2)+v_(y)^(2)) = sqrt((c)^(2)+(2bt)^(2)) = sqrt(c^(2)+4b^(2)t^(2))`