Unit 1: One-dimensional Motion

Physics Foundations:

  • vectors- magnitude/size AND DIRECTION is specified

    the direction as well as the distance is specified

  • scalars- magnitude/size

    magnitude/size is specified but no direction

Distance, Displacement, and Coordinate System:

  • distance- total length of your path

    • always absolute value (can never be negative)
    • is a scalar quantity with units of distance

  • displacement- net change in position

    • mentions change + direction
    • vector quantity with units of distance

  • formula for displacement:

  • position time graph- time is on horizontal axis & position is on vertical axis

    • ex of position time graph:

    on this graph t=time & the position is what number it is at

  • coordinate system- what we use to describe position

    • origin = 0
    • defines directions with positive & negative numbers

  • position- location of the object based on origin (0)

    • represented by x when referring to the position

  • reference frame: point of view from which measurements can be made where all frames of reference are equally valid

Average Velocity and Average Speed:

  • average velocity- is a vector

formula for average velocity:

  • average speed- is a scalar

formula for average speed:

Velocity and Speed from Graphs:

  • instantaneous speed- speed of an object at a particular moment in time

    • always absolute value (can never be negative)

  • instantaneous velocity- velocity at a particular moment

    • can be positive (+) or negative (-)

  • to be more exact you can choose a smaller displacement and shortter time interval

    1. case where velocity of object does not change: average velocity

      1. in that case average velocity = instantaneous velocity

    2. case where velocity of object is changing: motion on x-verses t-graph

      1. slope at any particular point = instantaneous velocity
      2. get instantaneous rate of when x is changing with respect to time (find slope using closest unit of time before and after)

    estimate the line only ONE point can touch the line

3. case where acceleration is constant

-kinematic formulas (explained further on)

-area under the velocity vs time curve = displacement

  • Instantaneous vs average (in general)
    • average = over time
    • instantaneous = a given moment

Average and Instantaneous Acceleration:

  • acceleration- change in velocity over time (is a vector quantity)

formula for acceleration:

change in velocity aka average velocity

  • Velocity vs time graph
    • vertical axis represents the velocity of the object
    • slope of the velocity graph represents acceleration of the object

formula/example:

  • slope is steep = object rapidly changing velocity
  • slope is hallow = object not changing velocity as rapidly
  • slope is negative/directed downwards = acceleration is negative
  • slope is positive/directed upwards = acceleration will be positive
    • (area under velocity graph/curve = displacement of the object)

\

  • Average acceleration- rate at which velocity changes over a specified interval
    • \

  • Unit: SI units of m/s^2
  • is a vector quantity (can be positive or negative)
  • speed of object remains same but changes direction = object accelerating
  • velocity and acceleration vectors point in opposite directions = object is slowing down
  • Instantaneous acceleration- rate at which velocity changes at a specific instance in time

Motion with Constant Acceleration

kinematic equations:

  • earth’s gravity = 9.8 m/s^2
  • acceleration is a constant line