Chapter 2
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Chapter 2. Describing Motion—kinematics in 1-D. Describing Motion. Mechanics —study of the motion of objects Kinematics —study of how objects move Dynamics —study of force and why objects move. Describing Motion. Translational motion moving without rotating (spinning)

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Chapter 2

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Chapter 2

Chapter 2

Describing Motion—kinematics in 1-D


Describing motion

Describing Motion

  • Mechanics—study of the motion of objects

    • Kinematics—study of how objects move

    • Dynamics—study of force and why objects move


Describing motion1

Describing Motion

  • Translational motion

    • moving without rotating (spinning)

  • Frame of Reference

    • portion of the universe to where all measurements are referred (point of view)


Distance vs displacement

Distance vs. Displacement

  • 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)


Distance vs displacement1

Distance vs. Displacement

  • Displacement

    • In 1-Dimension, direction can be defined as + or –

    • x = x2 – x1 = (final position) – (initial position)

    • independent of path taken


Speed vs velocity

Speed vs. Velocity

  • Speed—How far an object moves in a given time

    • Average speed = (distance traveled)/(time elapsed)

    • Scalar

    • units of meters per second (m/s)


Speed vs velocity1

Speed vs. Velocity

  • Velocity—how much position changes in a given time

    • Average velocity = displacement/(time elapsed)

    • v = x/t

    • vector


Speed vs velocity2

Speed vs. Velocity

  • 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

Acceleration

  • 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


Acceleration1

Acceleration


Motion at constant acceleration

Motion at Constant Acceleration

  • Variables

    • x0—initial position

    • x—final position

    • v0—initial velocity

    • v—final velocity

    • t—time (t0 usually = 0)

    • a—acceleration


Motion at constant acceleration1

Motion at Constant 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


Motion at constant acceleration2

Motion at Constant Acceleration

  • 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)


Graphical analysis of motion

Graphical Analysis of Motion

  • Position vs. time graphs

    • Horizontal line

    • Slanted straight line

    • Curved line


Graphical analysis of motion1

Graphical Analysis of Motion

  • Velocity vs. Time graphs

    • Horizontal line

    • Slanted straight line

    • Curved line


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