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Understanding Motion: The Physics of Distance, Speed, and Time Equations

This guide explores the fundamental physics equation d = vt, which relates distance, velocity, and time. Each variable in this equation represents a specific measurement: d for distance (meters), v for velocity or speed (meters/second), and t for time (seconds). Understanding how to manipulate these quantities and recognize the importance of units is essential in physics. We provide examples, unit conversions, and practice problems to reinforce learning. Mastering these concepts helps in solving real-world motion problems effectively.

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Understanding Motion: The Physics of Distance, Speed, and Time Equations

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  1. The math of Physics

  2. Equations d = v t • In physics, equations are used to show how different measured quantities are related • Each letter in this equation represents a different quantity or variable • d – distance (in meters, m) • v - velocity (or speed) (in meters per sec, m/s) • t – time (in seconds, s) • v and t are written next to each other, so that means they are multiplied together • d is all by itself on one side of the equal sign…… so this equation solves for d (distance) • written as a sentence ….“Distance is equal to speed multiplied by time”

  3. Units • Units (or labels) need to be included with all quantities • How tall are you? • 60 • ???? • Quantities make no sense without UNITS!!!

  4. Units behave like numbers! • Units behave like numbers • When a number is divided by itself, the number cancels out leaving a 1. • Any whole number can be written as a fraction with a 1 as the denominator

  5. See how numbers cancel…..

  6. Diagonals Cancel

  7. Units work the same way….

  8. Another example

  9. For any equation… • The Units must be the same on both sides of the equal sign Units on both sides of the equal sign are equal to ‘m’!!

  10. Motion formula --- d = v t Do units agree on both sides of each of these equations???

  11. Example Problem • A car travels at 5 m/s for 120 s. How far has the car travelled? • What are they asking for? • What do you have? • What equation is best? • Plug in and Solve!

  12. Example Problem 2 • A runner travelled 400 m in 80 s, how fast was the runner?? • What are they asking for? • What do you have? • What equation is best?

  13. Unit conversions • Conversion factors are used to cancel out unwanted units and acquire desired units • 1 yard = 3 feet • 150 ft = _______ yds • 1kg = 2.2 lbs • 50 kg = _____ lbs • 5280ft = 1 mi • 3000 ft = ________ mi

  14. More unit conversions • 1 N = .22 lbs • 7 lbs. = ________ • 1 km = 0.6 mi • 10 km = _____________ mi

  15. Standard (Fundamental) Units (SI) --- Metric Units

  16. Metric Prefix conversions • Important ones • Milli • Centi • ….. Base • Kilo

  17. Practice questions about Metric units • How many meters in a Kilometer? • How many centimeters in a meter? • How many millimeters in a meter? • How many grams in a kilogram? • 340 g = _________________ kg • 230 cm = _______________ m • 3.5 km = ________________ m • 4500 m = ________________ km

  18. Visualizing Units • Activity in library after in class demo’s.

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