Final answer:
A negatively charged particle placed at rest in an electric potential field that increases in the positive x-direction will accelerate in the positive x-direction.
Step-by-step explanation:
The negatively charged particle will accelerate in the positive x-direction when placed at rest in an electric potential field that increases in the positive x-direction. The force experienced by a charged particle in an electric field is given by F = qE, where F is the force, q is the charge, and E is the electric field strength. Since the particle has a negative charge, the force will be in the opposite direction of the electric field. Therefore, the particle will accelerate in the positive x-direction.