Position / Displacement

  • An object's position is its location at a given point in time

  • C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image010.png

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  • Position and displacement are both vectors

  • C:\25225E85\B09A51C6-0574-4A0C-A2C1-496768C10C63_files\image012.png

Average Speed

  • Average speed is the distance traveled divided by the time interval

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  • Average speed is a scalar, and is measured in meters/second

Average Velocity

  • Velocity is the rate at which position changes.

  • Average velocity is the displacement during a time interval divided by the time interval

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  • Average velocity is a vector, and is also measured in meter/second

Acceleration

  • Acceleration is the rate at which velocity changes

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  • Acceleration is a vector

  • Units are m/s2

The Position Vector

y(m) a? ËćÔ- FĆć) XC) Î Zr x(m) 123456789

Average Velocity

9 8 7 6 5 4 3 2 1 x(m) 1 Find the average velocity between 1 and 6 seconds. -2.5. - o.sE 5 rise t(s) 65 2 3 4 5 6 7 8 9

Instantaneous Velocity

  • Average velocity observed over an infinitely small time interval provides instantons velocity

  • Instantaneous velocity is the derivative of position with respect to time

    x(m) , slope 1234567 t(s)

  • Area under the velocity-time graph is the displacement during that time interval

    t(s) 123456789

Acceleration

  • Acceleration is the rate at which velocity changes

    v(m/s) Av a lim — At—O At Av dv dt d2x dt2 9 8 7 6 5 4 3 2 1 1 2 3 4 a 5 6 At 7 8 t(s) 9

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