## Curriculum Element: Understanding the Concept of Rate of Change

Return to Curriculum Elements »

**Author: **Professor Fary Sami, Harford Community College (fsami@harford.edu)

**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.

### Description

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.