2.7 Game 2302-0370 motion -- uniform and relative velocity

Table of contents

• Preface
  • General
  • Viewing tip
    • Figures
    • Listings
• General background information
• Discussion and sample code
  • A simple exercise on uniform velocity
  • An exercise on average velocity
  • Multiple concurrent velocities
    • Exercise #1 for a man on a train
    • Exercise #2 for a man on a train
    • An exercise with three vectors in a plane
• Run the scripts
• Miscellaneous

Preface

General

This module is part of a series of modules designed for teaching the physics component of GAME2302 Mathematical Applications for Game Development at Austin Community College in Austin, TX. (See GAME 2302-0100: Introduction for the first module in the course along with a description of the course,course resources, homework assignments, etc.)

The purpose of this module is to explain uniform velocity and relative velocity.

Viewing tip

I recommend that you open another copy of this document in a separate browser window and use the following links to easily find and view the Figuresand Listings while you are reading about them.

Figures

• Figure 1 . Screen output for Listing #1.
• Figure 2 . Vector diagram for the hockey puck.
• Figure 3 . Screen output for Listing #2.
• Figure 4 . Vector diagram for a man on a train.
• Figure 5 . Screen output for Listing #3.
• Figure 6 . Another vector diagram for a man on a train
• Figure 7 . Screen output for Exercise #2 for a man on a train.
• Figure 8 . Vector diagram for man on aircraft carrier.
• Figure 9 . Screen output for Listing #4.

Listings

• Listing 1 . A simple exercise on uniform velocity.
• Listing 2 . An exercise on average velocity.
• Listing 3 . Exercise #1 for a man on a train.
• Listing 4 . An exercise with three vectors in a plane.

General background information

What is velocity?

Velocity is the time rate of change of position . Since displacement is the change of position, velocity is also the rate of displacement . Since displacement is a vector quantity, velocity is also a vector quantity -- it hasmagnitude and direction.

An airplane may traverse 350 miles in a northeasterly direction in one hour. This statement describes a vector quantity (velocity) because it has bothmagnitude and direction.

The same airplane may traverse 350 miles in a southwesterly direction in one hour. This statement describes a different velocity. Even though the magnitudeis the same in both cases, the direction is different. Hence, the velocity is different.

What is speed?

Speed is distance covered in a unit of time without reference to direction. Since there is no reference to direction, speed is a scalar quantity.

A car may traverse 60 miles in one hour. An airplane may traverse 350 miles in one hour. An excellent runner may traverse one mile in three minutes. All ofthese statements describe scalar quantities (speed) since there is no reference to direction.

A person in a seat on a Ferris wheel may travel around the axle in the center of the wheel at a constant rotational speed. However, that person's velocity is notconstant. The velocity is continually changing because the direction of motion is continually changing.