Velocities: mean, average and instantaneous in uniform accelerated motion, some pedagogical comments

TL;DR

This paper explores the relationships among different types of velocities in uniformly accelerated motion and proposes pedagogical strategies to better teach this concept, emphasizing the connection between instantaneous, mean, and average velocities.

Contribution

It clarifies the relation between velocities evaluated at specific times and proposes an educational approach for teaching uniformly accelerated motion.

Findings

Instantaneous velocity at midpoint time resembles mean and average velocities.

Detailed explanation of the relations among different velocities.

Proposed pedagogical strategy for teaching accelerated motion.

Abstract

The relation among instantaneous, mean and average velocities in one-dimensional motion with constant acceleration is studied. It was shown that the instant velocity evaluated in the time $t_{p}=\left(t_2+t_1\right)/2$ is similar to the mean and average velocities evaluated between the times $t_1$ and $t_2$. The reason for relations illustrated before were shown in detail. Also, the results obtained were used to propose a pedagogical strategy in order to study the one-dimensional motion with constant acceleration as a natural extension of one-dimensional motion with constant velocity.