Question

if an object is accelerating, which of the following MUST be true?

The force is acting on the object.
The force is acting on the object.

The object is falling due to gravity.
The object is falling due to gravity.

The object is exerting a force on something.
The object is exerting a force on something.

The object is a projectile.

Answer 1

Only this MUST be true (in an inertial frame):

- A force is acting on the object. (More precisely: the net force on the object is nonzero.)

Not necessarily true:
- The object is falling due to gravity — no: acceleration can come from any force (push, tension, electric force, centripetal force, etc.), not only gravity.
- The object is a projectile — no: a projectile is a special case (only gravity acting); many accelerating objects are not projectiles.
- The object is exerting a force on something — caution: by Newton’s third law, whenever a force acts on the object there is an equal-and-opposite force exerted on whatever is applying the force, so in ordinary classical mechanics the object does exert a force on something. But that is a consequence of the first statement, not an independent requirement in the usual wording of this question.