Trajectories in the Classroom: Learning from Toy Cars

The most basic education in classical physics requires an understanding of one-dimensional and two-dimensional motion. These can be illustrated and analyzed through a variety of graphs. 

The topic of transportation is ideal for studying trajectory. Basic physics equations pertain to all types of transportation. 

Below are two examples of trajectories, the first modeled by a radio-controlled toy SUV and the second by a radio-controlled toy car. These graphs are excerpted from The Science of Cars: Volume 3 from Schottenbauer Publishing.

Discussion Questions

1. In how many dimensions does the SUV move? a) 1, b) 2, c) 3.
2. What is the total distance the SUV moves? 
3. What is the average velocity of the SUV?
4. What is the average acceleration of the SUV?
5. In how many dimensions does the car move? a) 1, b) 2, c) 3.
6. What is the total distance the car moves? 
7. What is the average velocity of the car?
8. What is the average acceleration of the car?

Additional Information

Schottenbauer Publishing

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The Hard Truth Regarding Gravity and Flight

In physical science and physics class, students learn that all objects fall at the same rate due to gravity. When learning that force equals mass times acceleration (F = ma), many students may question the assertion, due to many apparent contradictions. Here are a few:

• Why does a leaf fall slowly, while a ball falls quickly?
• Why does a parachute slow the rate of descent?
• Why do space rockets not fall back to earth when the engines stop?

Although there is no data about space travel in the book series Soar! The Science of Flight, there are plenty of graphs on the motion of objects moving in the lab:

Volume 1

• String Trolley
• Umbrella
• Plastic Bag
• Ball
• Pen
• Yardstick
• Paper Airplanes
• Radio-Controlled Helicopter

Volume 2

• Air Rocket
• Parachute
• Glider
• Kite

By comparing graphs of motion, students can estimate the effects of air resistance on various types of falling objects. In addition, direct measurement of force by an accelerometer are provided in some graphs within each book above, showing the acceleration due to gravity versus acceleration which describes changes in motion.

The following books from Schottenbauer Publishing contain graphs and data pertaining to the science of falling or flying objects:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Flight
• The Science of Archery & Shooting Sports
• The Science of Balls
• Sampler Edition: 24 Sports Balls Bouncing, Rolling, & Flying
• Volumes 3, 6, & 7
• Volume 8: Assorted Balls
• The Science of Baseball
• Gravity, Springs, & Collisions: Graphs of Classical Physics Experiments

Anthologies of 28 Graphs

• The Science of Transportation
• The Science of Ball Sports

Additional Information

Schottenbauer Publishing

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Boating in the Lab and on Natural Waterways

Transportation in real life often occurs in conditions which are not ideal. Laboratory studies initiated in traditional classrooms often simulate simple conditions, leaving the more complicated reality for advanced graduate studies and specialty laboratory research.

What are some of the differences between laboratory research and real conditions for transportation? The graphs below, excerpted from The Science of Floating & Boating: Volume 3 from Schottenbauer Publishing, show the differences between a ping pong ball floating in laboratory conditions and in a natural (outdoor) reservoir.

Discussion Questions

1. Which graph shows a sine wave? 
2. Which graph shows chaotic dynamics?
3. In Graph 1, the waves were most likely created by: a) an object moving up and down at a regular frequency, b) natural wind? 
4. In Graph 2, the waves were most likely created by: a) natural wind, b) a boat on the water? 
5. Describe the range of each graph, including the minimum and maximum of each line in each graph. 
6. Which graph demonstrates a larger variation (or order of magnitude) in motion? Why? 
7. On a separate piece of paper, draw the location of the ball as it moves in Graph 1. Include maximum and minimum points. What is the maximum physical distance moved between a consecutive trough and crest?
8. On a separate piece of paper, draw the location of the ball as it moves in Graph 2. Include at least 10 points, including maximum and minimum points on each line in the graph. What is the maximum physical distance moved between a consecutive trough and crest?

The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of fluid dynamics, water, and/or boats:

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Floating & Boating
• Volume 1: Force & Acceleration
• Volume 2: Force & Acceleration
• Volume 3: Video Analysis
• Fluid Dynamics & The Science of Natural Waterways
• Volume 1: Water Flow Meter & Video Analysis

Anthologies of 28 Graphs

• The Science of Transportation

Additional Information

Schottenbauer Publishing

Free Education Resources