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Understanding Motion: Models & Representations

Explore verbal & mathematical models, graphs, diagrams, and language to represent motion. Learn about scalar & vector quantities, time intervals, displacement, speed, and velocity equations. Step-by-step problem-solving approach included.

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Understanding Motion: Models & Representations

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  1. 4 Ways to Represent Motion

  2. 4 Representations of Motion • Verbal models (language) • Mathematical models (equations) • Graphs • Diagrams(motion maps)

  3. 1. Language • scalar – a quantity with only magnitude (a numeric value) but no direction (ex. time) • vector – a quantity with magnitude and direction • time interval (t) – a length of time • SI unit isseconds (s) • Scalar

  4. position (x) – the location of an object with respect to an origin • SI unit ismeters (m) • vector • displacement (Δx) – change in position • Δ Delta means change in • SI unit ismeters (m) • vector • Δx = xf – xi • Ex: Stew runs 4m to the right of his home then 7m left. What is his displacement from his home?

  5. average speed – the total distance traveled in an amount of time (Ex: 3 cm/s) • SI unit is meters second • Scalar speed = distance or v = d time t

  6. average velocity (vavg) – total displacement of an object in an amount of time • Speed with a direction (Ex: 3 cm/s south) • SI unit is meters second • Vector vavg = displacement or vavg = Δx time t

  7. 2. Mathematical Models(Equations) speed = distance or v = d time t velocity = displacement or v = Δx time t

  8. Steps to Solve a Problem • Draw a diagram of the situation • Identify given variables and unknowns • Convert Units • Write equation and WRITE IT without numbers • Substitute values and solve • Box answer with units (and direction)

  9. Example: A man runs 50 m to the west in 10.0 s, and then 30 m to the south in 6.0s. What is the magnitude of his average speed? (5 m/s) • Is this the same as his average velocity? • If he continues to run at this average speed, how far will he have travelled in 20 minutes? (6000m)

  10. Turn to Pg 44 in your text book.

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