Question

A charged particle is initially at rest moving from refrence point on x

Answer 1

It is not possible to keep charged particle at rest.

There are two reasons.

Thermal energy always keeps charged particle vibrating.

Electric field will give acceleration in one direction depending on the type of charge.

For your question the answer is

charged particle at rest needs these conditions: Temperature is absolute zero and either no electric field or balanced electric field.

Moving from reference point on x: Temperature is still at absolute zero and electric field is acting parallel to x-axis.

(Assumption: there is no magnetic field.)