Embodiments of the invention provide methods and apparatus to reduce the number of intersection tests required to determine if an object moving within a three-dimensional scene collides with any other objects. According to one embodiment of the invention, a physics engine may cast a velocity box into the scene and traverse the velocity box through an integrated acceleration data structure. By traversing the velocity box through an integrated acceleration data structure, a physics engine may determine which objects are in the same area of the scene and are likely intersect the velocity box. The physics engine may use the objects when performing intersection tests to reduce the number of intersection tests which are necessary to determine which objects intersect the velocity box. A reduction in the number of intersection tests may reduce the amount of time necessary to determine if a moving object collides with any other objects.