Final answer:
The tangential component of acceleration for a particle moving along a curve at constant speed is zero. Tangential acceleration changes the speed of an object, which does not occur in uniform circular motion with constant speed.
Step-by-step explanation:
If a particle moves along a curve with a constant speed, then its tangential component of acceleration is zero. The tangential acceleration describes the acceleration that is always tangential to the path it is moving along. In physics, particularly in the context of circular motion, the term tangential acceleration refers to changes in the speed of an object but not its direction, whereas centripetal acceleration refers to the necessary change in direction of the velocity without altering its magnitude.
When an object is moving in uniform circular motion, its velocity vector is constantly changing direction, which means it has centripetal acceleration. However, if the speed remains constant, that implies there is no tangential acceleration since tangential acceleration would imply a change in the speed, not just the direction. Hence, the tangential acceleration is zero in this scenario.