Question about inertia and frames of reference

Question

A ball inside a truck is not moving. Will the first Newton's law hold as seen by the observer inside the truck, if the truck suddenly accelerated forward? Explain your answer. Is this frame of reference inertial or non-inertial?

Similarly, is this frame of reference inertial or non-inertial as seen by the observer on the ground?

Answer 1

If the truck begins at rest and the ball sits in the middle of the truck, stationary to begin, will be an inertial frame of reference (truck and ball). Once the truck begins to accelerate in any direction, the reference frame of the ball relative to the truck becomes non-inertial, as the ball will roll in the direction that opposes the direction of acceleration. This thereby contradicts Newton’s first law, that an object at rest will stay at rest; Newton’s first law does not hold within non-inertial reference frames.

However, an observer watching this on the outside, standing stationary on the side of the road, will be in an inertial reference frame with respect to the ball. That is, since the observer on the ground is at rest, and the ball will seem to them as though it also remains at rest— it will remain in its initial position in space as observed by the observer. However, to an observer in the truck, the ball appears to move- that is because the reference frame itself is accelerating (non-inertial), and the truck is moving relative to the ball, so the ball appears to be moving in the direction opposite the trucks acceleration.