What are conditions necessary for reversal of direction of a particle performing 1D motion? When a particle reverses its direction while in 1D motion its velocity must be 0. But some other conditions are also necessary like acceleration should not be 0, etc. So can someone tell me some other conditions? (In terms of derivatives if possible)
 A: 
But some other condition are also necessary like acceleration should not be 0

Not true. Just imagine the motion characterized by $r(t)=\left(t-1\right)^4$. At $t=1$, there is a direction change and yet $v(1)$ and $a(1)$ are both zero.
The only condition for 1-D motion that guarantees there is a change in direction is when the velocity changes signs, either from $+$ to $-$ or the converse.
A: As @user256872 states the change in 1D direction occurs at a time where $v(t) = dr(t)/dt$ changes sign.
Note that $r(t)$ and $v(t)$ must be continuous in time to describe a valid path.  However, for idealized situations $a(t)$ can have discontinuities (steps) when forces are suddenly applied/removed. [Discontinuities in acceleration do not occur in real-world environments because of deformation, quantum mechanics effects, and other causes. However, a jump-discontinuity in acceleration and, accordingly, unbounded jerk are feasible in an idealized setting, such as an idealized point mass moving along a piecewise smooth, whole continuous path. The jump-discontinuity occurs at points where the path is not smooth. Extrapolating from these idealized settings, one can qualitatively describe, explain and predict the effects of jerk in real situations. (Wikipedia discussion of Jerk, https://en.wikipedia.org/wiki/Jerk_%28physics%29)]
