Which maneuver is fundamental to avoiding an obstacle quickly?

The maneuver that is fundamental to avoiding an obstacle quickly is quick braking and swift swerving to the side. This approach allows the rider to quickly reduce speed while also maneuvering the motorcycle away from the obstacle. Rapid braking helps to decrease the momentum of the motorcycle, making it more manageable to change direction effectively. Swiftly swerving to the side enables the rider to avoid the obstacle without losing control of the bike.

In emergency situations, having the ability to combine both braking and maneuvering is critical. It ensures that the motorcycle can be stopped or redirected in a controlled manner, thus minimizing the risk of a collision or an accident. Quick braking can also shift the center of gravity, allowing for better handling and balance during the maneuver.

Other options may not provide the same level of quick response. Gradual acceleration and lateral movement would take too long to execute in a sudden emergency. Engine revving while abruptly stopping could lead to loss of control. Similarly, turning the handlebars while slowing down does not prioritize the necessary immediate reactions to avoid a potential hazard quickly.