Final answer:
An object at rest cannot have acceleration since acceleration requires a change in velocity over time. In the context of collisions, momentum is always conserved, but kinetic energy is only conserved in elastic collisions.
Step-by-step explanation:
Can an object be at rest and still have acceleration? The answer to this question is No. In physics, for an object to have acceleration, there must be a change in its velocity over time. When an object is at rest and remains at rest, its velocity does not change, meaning there is no acceleration. However, if at some moment while at rest, a force is applied and the object begins to change its state of motion, then we could say it has acceleration, but this is not the case while the object remains at rest.
As an example, consider a ball lying on the ground. If no forces are acting on it, such as being kicked or picked up, it has zero acceleration because its velocity remains zero. The velocity of an object includes both speed and direction, so even an object moving at a constant speed in a circular path (uniform circular motion) is accelerating because its direction is constantly changing, despite the speed being constant.
In the context of a collision, when two objects of equal mass collide, and one goes from moving to at rest while the other moves with some velocity, momentum is conserved. This is because momentum depends on both mass and velocity, and assuming no external forces, the momentum before and after the collision for the entire system is the same. However, kinetic energy may not be conserved unless the collision is elastic (an idealized type of collision where no kinetic energy is lost).