Ohio Assessments for Educators (OAE) Mathematics Practice Exam

The derivative of a position function gives you which variable?

1. Acceleration

2. Velocity

3. Distance

4. Speed

The correct answer is: Velocity

The derivative of a position function represents the rate of change of position with respect to time. This rate of change is defined as velocity. When you take the derivative of the position function, you are calculating how quickly the object's position changes over time, which is precisely the definition of velocity. Velocity is a vector quantity, meaning it has both magnitude and direction, and it tells you not only how fast an object is moving but also in which direction. Understanding this concept is crucial in physics and mathematics, as it lays the foundation for analyzing motion. The other options, such as acceleration, distance, and speed, relate to motion but are derived from different processes. For instance, acceleration is the derivative of velocity, while distance is related to the position but not directly to the derivative of the position function. Speed, while it deals with the magnitude of velocity, is not a direct result of taking the derivative of position. Thus, identifying the derivative of the position function as velocity is fundamental in the study of motion.