Momentum Conservation in an Accelerating Coordinate System

[Karol]

Homework Statement

A ball of mass m travels with speed v, hits a stationary ball with the same mass m and after collision they both move at speed v/2.
From the point of view of the first ball the total momentum is -mv and after the collision it is 0. why isn't the law of conservation of momentum valid for this coordinate system?

Homework Equations

The first and second laws of Newton, F=ma and that a body is at rest while no forces act on it are valid in all coordinate systems moving at constant speed.

The Attempt at a Solution

The coordinate system has acceleration during the collision so F=ma isn't valid. i don't know to continue from here and i guess it's the right answer, no?

 

[Doc Al]

Sounds good to me. The coordinate system attached to the first ball is not an inertial reference frame.