Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What does velocity represent in calculus?

1. Second derivative

2. First derivative

3. Integral

4. Constant

The correct answer is: First derivative

Velocity represents the rate of change of displacement with respect to time. In calculus, this relationship is captured by the first derivative of the position function. When you take the derivative of the position function (which gives the location of an object over time), you obtain the velocity function. This function provides insights into how fast the position of an object is changing at any given moment. The concept stems from the fundamental principles of calculus, where derivatives quantify the idea of instantaneous rates of change. For example, if you have a position function that describes the path of a moving object, calculating the first derivative of that function yields the velocity, indicating how quickly the object is moving and in which direction at any specific time. In contrast, the second derivative would represent acceleration, the integral relates to the accumulated area under a curve (which can give information about distance traveled over time), and a constant does not convey any information about changes in position over time. Understanding velocity as the first derivative is crucial for studies in calculus, particularly in physics and engineering contexts.