2.8 Game 2302-0380 motion -- variable velocity and acceleration

Table of contents

• Preface
  • General
  • Viewing tip
    • Figures
    • Listings
• General background information
  • Variable velocity
  • Acceleration
  • The acceleration of gravity
• Discussion and sample code
  • Variable velocity exercise #1
  • Variable velocity exercise #2
  • Acceleration of gravity exercise #1
  • Acceleration of gravity exercise #2
  • Acceleration of gravity exercise #3
  • Other useful equations
    • Exercise to find the velocity
    • Exercise to find the height
• 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 variable velocity and acceleration.

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 . Graph for variable velocity exercise #1.
• Figure 2 . Screen output for Listing #1.
• Figure 3 . Displacement versus time for first five time intervals.
• Figure 4 . Screen output for Listing #2.
• Figure 5 . Screen output for Listing #3.
• Figure 6 . Screen output for Listing #4 at 45 degrees.
• Figure 7 . Trajectory for two different firing angles.
• Figure 8 . Screen output for Listing #4 at 60 degrees.
• Figure 9 . Screen output for Listing #5.
• Figure 10 . Screen output for Listing #6.
• Figure 11 . Screen output for Listing #7.

Listings

• Listing 1 . Variable velocity exercise #1.
• Listing 2 . Variable velocity exercise #2.
• Listing 3 . Acceleration of gravity exercise #1.
• Listing 4 . Acceleration of gravity exercise #2.
• Listing 5 . Acceleration of gravity exercise #3.
• Listing 6 . Exercise to find the velocity.
• Listing 7 . Exercise to find the height.

General background information

I will provide an introduction to variable velocity, acceleration, and the acceleration of gravity in thissection. I will provide exercises on those topics in the next section.

Variable velocity

What is velocity?

To review, you learned in an earlier module that velocity is the rate of change of position. Since displacement is a change in position, velocity is alsothe rate of displacement.

Uniform versus variable velocity

Previous modules have dealt exclusively with uniform velocity. However, many situations in life involve variable velocity and acceleration. For example, thesimple act of stopping an automobile at a traffic light and then resuming the trip once the light turns green involves variable velocity and acceleration.

Three equations

I will explain both of these topics in this module using three well-known physics equations that deal with the displacement of a projectile in a vacuum under the influence of gravity .

The equation that we will spend the most time on is

h = v0*t + 0.5*g*t^2