Curriculum Element: Understanding the Concept of Rate of Change

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Author: Professor Fary Sami, Harford Community College (

Short Description: This activity helps students to visualize the differences between velocity and acceleration, using an applet to measure the rate of change of a dropping object. These simulations can be performed on Microsoft Excel, Matlab or Mathematica.

Implementation Levels: Calculus. Examples: Calculus I (MATH 203) at Harford Community College; Calculus I (MATH 140) at the University of Maryland.


Students often find it a challenge to visualize the relationship between position, velocity and acceleration, and differences between velocity and acceleration. This curriculum element provides an excellent opportunity for students to collect and analyze data and in the process understand how derivatives can be used to predict and understand the behavior of real systems. Students will use an applet to simulate a falling object, collect data on the position of the object at different time points and identify best fit curves for both position and velocity as a function of time. Furthermore, students can be asked to estimate the velocity and acceleration of the falling object over time and critically comment on the rates of changes, using the data. The use of applet and data analyses can be performed in Microsoft Excel, Matlab or Mathematica. This activity provides an opportunity to discuss applications of the concept of rate of change to real life scenarios. The students’ feedback was positive and largely commented on the advantage of working with data and critically analyzing it as a means to understand the concept of rate of change. The activity sheet and the student feedback form can be accessed below.