Question

Is it possible to move on a curved path with constant acceleration

Answer 1

No it is not possible to move along a circular path wiyh constant acc.

Answer 2

acceleration is velocity in unit time..velocity is a vector quantity- magnitude and DIRECTION

while moving in a curved path , the direction changes.if direction changes ,the velocity also changes because velocity is vector. now velocity changes..since acceleration is velocity in unit time, this change in velocity will change the acceleration..so ,no uniform acceleration in a curved path