The coordinates of a particle moving in x-y plane at any instant of time t are x `x = 4 t ^(2), y = 3t ^(2).` The speed of the particle at that instant is

Options

A. `10 t `
B. `5t`
C. `3t`
D. `2t `

Answer

A

Explanation

`x = 4t ^(2)`
Differenctiate with respect to t, we get
`v _(x) = (dx)/(dt) = 2 xx 4t =8t`
Similarly, `v _(y) = (dy)/(dt) = 2 xx 3t = 6t`
The speed of the particle
`v = sqrt (v _(x) ^(2) + v _(y) ^(2))`
`= sqrt ((8t) ^(2) + (6t) ^(2))`
`= sqrt (64 t ^(2) + 36 t ^(2))`
`= sqrt ( 100 t ^(2)) = 10 t `