For a particle moving in a straight line If the velocity is zero for a time interval, is the acceleration zero at any instant within the time interval ?
 A: If the time interval you are talking about is any infinitesimally small period, then acceleration doesn't have to be zero. (Think of a projectile reaching its highest height or an oscillator reaching its extreme distance with respect to the equilibrium point; in both cases the object is momentarily stationary yet you cannot say its acceleration is zero at those exact instances). But, for a finite period (which is mostly the case in real world) acceleration will be zero. So, the answer practically will be "Yes, acceleration of the object, in the time period during which velocity is zero, will be zero."
A: As per the practical sense, any question related to velocity is relative, so please specify the direction. Now, defining the situation in theory we can say that even a stationary object is mathematically experiencing acceleration from every direction equably. 
A: Just invoke the most powerful principle in physics: Newton's first law of motion! A body will remain at rest or will not change its state of motion, unless acted on by a non-zero net external force. That combined with the second law, $\vec{F}_{\text{net}}=\frac{d\vec{p}}{dt}$, gives you the answer inmediately, without the use of any example.
If you are in the context of quantum mechanics and relativity, what you call a force and the classical concept of velocity lose their meaning, so it's not worth going into that.
A: The acceleration on an object is the derivative of its velocity. So if velocity is zero (or any other constant) over a time interval, the acceleration is zero over the whole interval.
