Question

change in potential energy of a system is the work done by an external agent in moving the charge slowly without causing acceleration. why slowly and why should there be no acceleration .

Answer 1

change in acceleration causes change in speed ,which inturn results in change in energy .this change in energy is due to change in acceleration .
but if we does work on the charge without acceleration the change is energy is only due to the change in position .all other characters are the same i.e speed etc is same.

but in earlier case change in energy is due to both change in position and change in speed .

​we know potential energy depends only on position .thus work is done without acceleration and slowly