Final answer:
Three out of the six statements presented are true, while the others are false. The true statements align with Newton's laws of motion, which describe the relationship between objects and the forces that act upon them.
Step-by-step explanation:
Let's address each statement to determine its truthfulness:
(a) An object can move even when no force acts on it. This statement is true under Newton's first law of motion, also known as the law of inertia. An object in motion continues to move at a constant velocity in a straight line unless acted upon by a net external force.
(b) If an object isn't moving, no external forces act on it. This statement is false. An object may be at rest because the net external force on it is zero, not necessarily because no external forces are acting on it.
(c) If a single force acts on an object, the object accelerates. This is true; according to Newton's second law of motion, a net unbalanced force acting on an object causes it to accelerate.
(d) If an object accelerates, a force is acting on it. This is true; acceleration implies a change in velocity, which according to Newton's second law, results from a net external force.
(e) If an object isn't accelerating, no external force is acting on it. This statement is false. An object may experience multiple forces that cancel each other out, resulting in no acceleration, even though external forces may be present.
(f) If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction. This statement is false. The object will accelerate in the positive x-direction, but depending on its initial velocity, it may not move solely in that direction.
Examples and further explanations:
- Net external force: A net external force results in an acceleration of a system, not necessarily in the direction of motion. This force is vital when we consider Newton's second law.
- Uniform circular motion: An object in uniform circular motion is indeed accelerating, and therefore, a net force acts on it, directed towards the center of the circle.
- Constant velocity: An object can travel at constant velocity if the net external force is zero. This can occur when all applied forces cancel out, resulting in no acceleration.