if action and reaction are always equal and opposite, why don't they always cancel each other and leave no force for acceleration of the body?
This is a great question and it's related to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The fact that action and reaction forces are equal and opposite is indeed true, but it doesn't mean they always cancel each other out and leave no force for acceleration. Allow me to explain why.
When two objects interact, such as when a person pushes against a wall, the person exerts a force on the wall, and simultaneously, the wall exerts an equal and opposite force back on the person. These forces act on different objects and are of the same magnitude but in opposite directions.
Now, while the forces are balanced, meaning they cancel each other out in terms of the net force on the system, they don't cancel out within each individual object. The force exerted by the person on the wall cannot cancel the force exerted by the wall on the person because these forces act on different objects.
In terms of acceleration, Newton's second law of motion comes into play. This law tells us that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. So, even if the action and reaction forces are equal, they can still result in an acceleration if the mass of the object is not zero.
To put it simply, imagine a person standing on a skateboard and pushing off a wall. While the force they exert on the wall is equal and opposite to the reaction force from the wall, the person will still accelerate because their mass is not zero. The equal and opposite forces maintain equilibrium, but as the person interacts with the wall, the direction of the forces changes, resulting in an overall motion.
In summary, while action and reaction forces are equal and opposite, they act on different objects and cannot cancel each other out entirely. The acceleration of an object depends on the net force acting on it, considering both external forces and the object's mass.