A particle with specific charge `q//m` moves rectilinerarly due to an electric field `E = E_(0) - ax`, where `a` is a positive constant, `x` is the distance from the point where the particle was initially at rest. Find:
(a) the distance covered by the particle till the moment it came to a standstill,
(b) the acceleration of the particle at that moment.

Explanation

The equaction of motion is,
`(dv)/(dt) = v (dv)/(dx) = (q)/(m) (E_(0) - ax)`
Intergrating
`(1)/(2) v^(2) - (q)/(m) (E_(0) x - (1)/(2) ax^(2))` = constant.
But initallty `v = 0` when `x = 0`, so "constant" = 0
Thus, `v^(2) = (2q)/(m) (E_(0) x - (1)/(2) ax^(2))`
Thus, `v = 0` again for `x = x_(m) = (2 E_(0))/(a)`
The corresponding accleration is,
`((dv)/(dt))_(x_(m)) = (q)/(m) (E_(0) - 2 E_(0)) = - (q E_(0))/(m)`