Kinematics in One Dimension: Classical Mechanics Study

1. Kinematics in One-Dimension

2. Kinematics in One-Dimension • Sections Covered – Honors Physics • Chapter 3: pages 42 – 60 • Chapter 5: pages 80 – 107 • Topics Covered • Position and time • Average speed and average velocity • Instantaneous velocity • Average acceleration • Kinematic formulas and problem solving • Graphical analysis • Free fall and acceleration of gravity

3. A Study in the Classics • *Classical Mechanics – the study of the motion of objects (force, energy, rotation, momentum…etc) • *Kinematics – Description of how objects move. • *Dynamics – Study of forces and their affects.

4. Time •  Time (t) • SI Units: Seconds (s) • SI Units: Metric *International System of Units • Instantaneous Time – A specific or instant time.

5. Intervals • Time Intervals – a time of duration, how long? Variable: Δt • Delta (Δ) – Greek letter, means ‘change in’. • Δ = final value – initial value

6. Scalar vs. Vector • Scalar - Quantity described by magnitude only • Vector – Quantity described by magnitude AND direction *What is Magnitude?! Magnitude = Numerical Amount

7. Position • Position - where an object is at a particular moment Variables = x, y, z • Change in Position: Δx, Δy, or Δz SI Units: Meters (m)

8. Displacement • Displacement –the shortest straight-line distance between the two points regardless of the path. • VECTOR quantity Change in Position: Δx = B - A Δx = xf - xo B *Note: Many times the subscript o is used for initial quantities A

9. Distance • Distance - Total path between two points with the route traveled taken into account. • SCALAR value SI Units: Meters (m) *Can Distance Be Negative? No, it’s considered an absolute value B A

10. Positive and Negative Positive = Large Negative = Small • Positive and negative signs are indications of direction, NOT magnitude. WRONG!

11. Average Speed Average Speed = *Distance is a quantity scalar *Speed is a quantity scalar SI Units: meters (m) m = = s seconds (s)

12. Average Velocity Average Velocity = *Displacement is a quantity vector meters (m) m *Velocity is a quantity vector = = s seconds (s) SI Units:

13. *Velocity vs. Speed Road Trip!! Car A decides to go to Memphis for some blues and BBQ (approx. 725 miles) Car B decides to go to Chicago for some pizza and a Cubs game (approx. 725 miles) Both cars arrive at their destination at the same time. Did the cars have the same velocity? Did the cars have the same speed?

14. Example 1 The position of a runner is plotted as a function of time, moving along the x-axis. He moves from an initial position xo = 50.0 m to a position xf = 30.5 m in a time of 3.00 s. What is his average velocity?

15. Example 2 A person jogs eight complete laps around a quarter mile track in a total of 12.5 minutes. Calculate: • The average speed • The average velocity

16. Example 3 Acar goes down a certain road at an average speed of 40 km/h and returns along the same road at an average speed of 60 km/h.  Calculate the average speed in km/h for the round trip.

17. Average Acceleration • Average Acceleration = Change in velocity over the change in time. Variable: • Average Acceleration is a vector quantity SI Units: m/s = = s

18. Positive and Negative Accelerations • A positive acceleration ≠ (necessarily) getting faster • A negative acceleration ≠ (necessarily) slowing down. • Positive acceleration simply means accelerating in a positive direction • Negative acceleration simply means accelerating in a negative direction.