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.

A particle with specific charge `q//m` moves rectilinerarly due to an

1.	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.
Answer» 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)`

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