Tutorial details

The pretest illustrates a general failure of students to apply the operational definitions of velocity and acceleration. The tutorial helps guide students to apply the definitions and to consider the idea of limits in the context of vector subtraction. Students consider the displacement, velocity and acceleration for an object moving around an oval track, first with constant speed and then with increasing speed. The case of decreasing speed is covered in the homework.

The students begin by considering successive positions and displacements of the object as it moves with constant speed around the track. They then consider how the direction of the velocity changes as the time interval between successive displacements becomes smaller and smaller. They recognize that in the limit that ∆t approaches zero, the velocity lies along the tangent to the trajectory. Students then consider changes in the velocity and come to recognize that, although the velocity vector does not change in magnitude, the change in velocity vector is not zero and thus, the acceleration is not zero.

In the process of constructing vectors to represent the motion for constant speed and then for increasing speed, students generalize their results to understand how the angle between the velocity and acceleration depends on the motion of the object. They come to recognize that the angle is less than 90° when the object is speeding up, greater than 90° when it is slowing down, and equal to 90° when it is moving with constant speed.

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Prerequisite tutorials

The Acceleration in one-dimension tutorial is a prerequisite to Motion in two dimensions.

Other prerequisites

Students should be familiar with the concepts of velocity and acceleration and with vector addition. It is not required that uniform circular motion has been covered in class. This tutorial can be very difficult for students. The third section on acceleration for motion with changing speed need not be used with all student populations.

It can be useful for students to have worked through the tutorial "Acceleration in one dimension."

Equipment

List

• straight edge
• white board or large sheet of paper with markers

Discussion