Is it possible for an object’s instantaneous velocity and instantaneous acceleration to be of opposite sign at some instant of time?

Yes

Explanation:

First Example:

- Throwing the ball up in the air with an upward velocity e.g 5 m/s. The ball moves in the direction of velocity. While the acceleration due to gravity is g = -9.81 m/s^2 is pointing downwards throughout the journey.

Second Example:

- The car at a certain speed decelerates down the road. It has certain positive velocity but after the driver applies or car slows down the acceleration is in the opposite direction to the motion or negative.  

a displacement distance is size of displ