How to Teach Acceleration Velocity in Middle School

Teaching velocity and acceleration in middle school is a fairly straightforward affair. Because calculus is not taught until high school it is appropriate only to teach the concepts of average velocity and acceleration as opposed to instantaneous velocity and acceleration. These calculations require the application of the principles of derivatives and differentiation. Average velocity and acceleration represent the average speed over an entire interval of time as opposed to individual moments. This is an important distinction to be made clear to students when first being introduced to this material.

Instructions

Teaching Velocity

1. Explain to your students that the concept of velocity is defined as the ratio of the change in position of an object, its displacement, during a particular time period. The equation (x2 - x1) / (t2 - t1) defines the average velocity of an object where x2 is the end position and x1 is the beginning position of the object. While t2 is the stop time and t1 is the start time of the object.

2. Create a coordinate graph where the x-axis is the time frame, in seconds, and the y-axis is the distance traveled, in meters. The x-axis begins at zero and moves, in the positive direction, at 1-second intervals. The y-axis can be negative or positive and measured in 1-meter intervals.

3. Instruct your students to imagine a car stopped 5 meters behind a start line. Mark this position on the graph at the point (0, -5). Then explain that the car speeds up and returns to rest during a time interval of, say, 4 seconds. In that 4 seconds the car travels a total of 8 meters.

4. Mark the end position of the car at the point (4, 3). Explain that the car passed the start line, y = 0, at the 3 second point. Mark this position on the graph at point (3, 0). This allows for easier tracing of the graph.

5. Draw a curve connecting these points. Use the equation for average velocity to show how fast the car was moving, on average, during the 4 second time interval. Write out (2 - (-5)) / (4 - 0) = (7 / 4) = 1.75. Explain that this means that car was moving at an average rate of 1.75 meters per second during the 4-second time period.

Teaching Acceleration

1. Refer back to the work with average velocity and explain that determining average acceleration is exactly the same as finding average velocity except that the ratio is of the change in velocity during a time interval instead of the change in position.

2. Use distance/time graph to create a graph for velocity/time. The x-axis remains as the time frame but the y-axis now represents velocity in meters per second (m/s).

3. Solve for average velocity at the starting point, x-intercept point and end point of the journey. You already know 2 of these points because when an object is at rest, in this case at t = 0, the velocity is equal to zero. Also, having solved for the end point when describing velocity, you know velocity at 4 seconds equals 1.75 meters per second. Solving for x = 3 gives: (0 - (-5)) / (3 - 0) = (5 / 3) = 1.667.

4. Label the appropriate points on the velocity/time graph: (0, 0), (3, 1.667), (4, 1.75). Explain that these are the points describing the velocity of the object at specified times. Draw a curve to connect the points.

5. Explain that to solve for acceleration you must now divide the change in velocity over the change in time. So, instead of (x2 - x1) / (t2 - t1) used to find velocity, you now use (v2 - v1) / (t2 - t1) to solve for acceleration. So, the acceleration equation becomes: (1.75 - 0) / 4 - 0) = (1.75 / 4) = .44. Explain to your students that this means the acceleration of the car during the 4-second time interval was .44 meters per second squared (m/s)^2.

References

• Physics Classroom: Speed and Velocity
• Physics Classroom: Acceleration