How can anything accelerate if every force has and equal and opposite counterpart?

The principle that every force has an equal and opposite counterpart, known as Newton's third law of motion, is indeed one of the fundamental principles of physics. However, it does not prevent objects from accelerating. Let me explain how an object can still accelerate despite this law.

In order to understand this, we need to consider the forces that are acting on the object. When an object experiences a force, it applies an equal and opposite force on the other object, as stated by Newton's third law. These forces always act on different objects, not on the same object.

So, when we talk about the acceleration of an object, we need to consider the net force acting on it. The net force is the vector sum of all the forces acting on the object. If the net force is non-zero, the object will experience an acceleration in the direction of the net force.

For example, consider a car moving forward and encountering air resistance. The car experiences a forward force from its engine, but it also experiences a backward force due to air resistance. According to Newton's third law, the air also experiences an equal and opposite force from the car. However, the net force on the car is still forward since the force from the engine is greater than the force of air resistance. This results in the car accelerating forward.

Similarly, an object can accelerate due to the force of gravity. When an apple falls from a tree, it experiences a gravitational force pulling it downward, but it also exerts an equal and opposite force on the Earth, pulling it slightly upward. However, the Earth's mass is so much larger than the apple that the effect on its motion is negligible.

In summary, while every force has an equal and opposite counterpart according to Newton's third law, it's the net force acting on an object that determines its acceleration. If the net force is non-zero, the object will accelerate in the direction of the net force, regardless of the presence of opposing forces.