The reation between the time t and position x for a particle moving on x-axis is given by `t=px^(2)+qx`, where p and q are constants. The relation between velocity v and acceleration a is as

Options

A. `a prop v^(3)`
B. `a prop v^(2)`
C. `a prop v^(4)`
D. `a prop v`

Answer

A

Explanation

`(dt)/(dx) = 2px + q`
`rarr v = (dx)/(dt) = (1)/(2px + q)`
`a = (-2p)/((2px + q)^(3)) rarr a prop ((1)/(2px + q))^(3)`
`rArr a prop v^(3)`