For motion of an object along the x-axis the velocity `v` dipends on the displacement `x` an `v=3x^(2)`, then what is the acceleration at `x=2 m`.

Options

A. `48 ms^(-2)`
B. `80 ms^(-2) m`.
C. `18 ms^(-2)`
D. `10 ms^(-2)`

Answer

B

Explanation

Given `v=3x^(2)-2x`, differentiating `v`, we get
`(dv)/(dt) =(6x -2) (dx)/(dt) =(6x -2) v`
` rArr a =(6xx 2 -2 ) (3x^(2)-2x)`
Now put `x=2 m`
`rArr a =(6 xx 2-2) (3(2)^(2)-2xx2)=80 ms^(-2)`.