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Chapter 2

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Chapter 2

Describing Motion—kinematics in 1-D

- Mechanics—study of the motion of objects
- Kinematics—study of how objects move
- Dynamics—study of force and why objects move

- Translational motion
- moving without rotating (spinning)

- Frame of Reference
- portion of the universe to where all measurements are referred (point of view)

- Distance (d)—a measure of length traveled
- Scalar—Magnitude only (20 m)

- Displacement(x)—change in position
- Vector—Magnitude (20 m) and a direction (North)

- Displacement
- In 1-Dimension, direction can be defined as + or –
- x = x2 – x1 = (final position) – (initial position)
- independent of path taken

- Speed—How far an object moves in a given time
- Average speed = (distance traveled)/(time elapsed)
- Scalar
- units of meters per second (m/s)

- Velocity—how much position changes in a given time
- Average velocity = displacement/(time elapsed)
- v = x/t
- vector

- Instantaneous velocity—velocity at one instant in time
- Average velocity over an infinitesimally small time interval
- Mathematically, the limit as t 0
- Instantaneous speed is the same magnitude as instantaneous velocity

- Acceleration (a)—change of velocity over a given time
- a = v/t
- Vector
- units of meters per second per second(m/s2)
- instantaneous acceleration, limit as t 0

- Variables
- x0—initial position
- x—final position
- v0—initial velocity
- v—final velocity
- t—time (t0 usually = 0)
- a—acceleration

- Principal Kinematic Equations
- v = v0 + at
- Useful when no position given

- x = x0 + v0t + ½ at2
- Useful when no final velocity given

- v2 = v02 + 2a(x – x0)
- Useful when no time given

- v = v0 + at

- Falling objects (y-axis movement)
- Position can be y and y0 instead of x and x0
- In a vacuum (no air resistance) all objects fall at the same rate due to gravity
- ag = -9.80 m/s2 (acceleration of gravity)

- Position vs. time graphs
- Horizontal line
- Slanted straight line
- Curved line

- Velocity vs. Time graphs
- Horizontal line
- Slanted straight line
- Curved line