A particle move a distance `x` in time `t` according to equation `x = (t + 5)^-1`. The acceleration of particle is alphaortional to.

Options

A. `("distance")^(-2)`
B. `("velocity")^((2)/(3))`
C. `("velocity")^((3//2))`
D. `("distance")^(2)`

Answer

C

Explanation

displaceement `x=(1)/((t+5))`
Acceleration `(dx)/(dt)=(-1)/((t+5)^(2))=-x^(2)`
`v=-x^(2)`
`(dv)/(dt)=-2x(dx)/(dt)`
`a=-2xv`
`=-2x(-x^(2))`
`a=2x^(3)`
`=2[(-v)^(1//2)]^(3)`
`a=2(-v)^(3//2)`
`a prop v^(3//2)`