If the velocity of a particle is given by `v=(180-16x)^((1)/(2))(m)/(s)`, then its acceleration will be

Options

A. zero
B. `8 m//s^2`
C. `-8 m//s^2`
D. `4 m//s^2 `

Answer

C

Explanation

`v = (180 - 16x )^(1/2)`
`a = (dv)/(dt) = 1/2 (180 - 16x)^(1/2 - 1) (-16) (dx)/(dt)`
`= (-8)/((180-16x)^(1/2)) xx (180 - 16x)^(1/2) = -8m//s^2`