As a high school football player, prior to taking Physics but aware of the concept of F = ma, I was convinced that I could maximize the force impacted upon an opponent (whether while tackling the ball carrier or being the ball carrier and breaking a tackle) by accelerating just prior to contact.
The person I mentioned this to, having already taken Physics, paused for a moment and, with what can only be described as an intentionally blank look on his face, replied, "... it doesn't really work that way."
I was convinced that he was wrong and I was correct. After all, F = ma, and my mass is staying constant, so if I accelerate, the force will naturally be greater. This, it appeared, was a simple scientific/mathematical truth and any confusion one may have would be due to their own limitations.
I now view the conceptual difficulty as similar to the one posed by the question, "If the forces are equal and opposite, why does anything happen at all? Why don't they just cancel each other out?"
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