Final answer:
Proper acceleration involves an increase in speed and centripetal force with a decrease in the radius of curvature. It is described in the context of an object in circular motion where centripetal acceleration increases when the radius of curvature decreases.
Step-by-step explanation:
The student's question appears to describe proper acceleration, which involves increases in both speed and centripetal force, with an accompanying decrease in the degree of radius of curvature. We understand from physics that centripetal acceleration is inversely proportional to the radius of curvature, meaning that it increases when the radius of curvature decreases. An object in circular motion experiences both tangential acceleration (changes in velocity magnitude) and centripetal acceleration (changes in the direction of velocity) which are perpendicular and independent of each other. Centripetal acceleration does not affect the magnitude of velocity, only its direction.
Acceleration in general can be caused by a change in magnitude or direction of velocity. Instantaneous acceleration is the acceleration at a specific instant, whereas deceleration refers to acceleration in the direction opposite to the velocity. Therefore, proper acceleration would involve an increase in speed (tangential acceleration) and an increase in centripetal force as the radius decreases, leading to a sharper curve (decrease in radius of curvature).