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 The branch of physics involving the motion of an object and the
relationship between that motion and other physics concepts
 Kinematics is a part of dynamics
 In kinematics, you are interested in the description of motion
 Not concerned with the cause of the motion

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 Sumaria and Egypt
 Mainly motion of heavenly bodies
 Greeks
 Also to understand the motion of heavenly bodies
 Systematic and detailed studies

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 Galileo
 Made astronomical observations with a telescope
 Experimental evidence for description of motion
 Quantitative study of motion

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 Defined in terms of a frame of reference
 One dimensional, so generally the x or yaxis

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 Vector quantities need both magnitude (size) and direction to completely
describe them
 Represented by an arrow, the length of the arrow is proportional to the
magnitude of the vector
 Head of the arrow represents the direction
 Generally printed in bold face type

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 Scalar quantities are completely described by magnitude only
 Mass
 Time
 Speed
 Distance

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 Measures the change in position
 Represented as Dx (if
horizontal) or Dy (if
vertical)
 Vector quantity
 + or  is generally sufficient to indicate direction for
onedimensional motion
 Units are meters (m) in SI, centimeters (cm) in cgs or feet (ft) in US
Customary

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 Distance may be, but is not necessarily, the magnitude of the
displacement
 Blue line shows the distance
 Red line shows the displacement

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 It takes time for an object to undergo a displacement
 The average velocity is rate at which the displacement occurs
 generally use a time interval, so let t_{i} = 0

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 Direction will be the same as the direction of the displacement (time
interval is always positive)
 Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.)
 Other units may be given in a problem, but generally will need to be
converted to these

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 Speed is a scalar quantity
 same units as velocity
 total distance / total time
 May be, but is not necessarily, the magnitude of the velocity

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 The limit of the average velocity as the time interval becomes
infinitesimally short, or as the time interval approaches zero
 The instantaneous velocity indicates what is happening at every point of
time

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 Uniform velocity is constant velocity
 The instantaneous velocities are always the same
 All the instantaneous velocities will also equal the average velocity

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 Velocity can be determined from a positiontime graph
 Average velocity equals the slope of the line joining the initial and
final positions
 Instantaneous velocity is the slope of the tangent to the curve at the
time of interest
 The instantaneous speed is the magnitude of the instantaneous velocity

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 Changing velocity (nonuniform) means an acceleration is present
 Acceleration is the rate of change of the velocity
 Units are m/s² (SI), cm/s² (cgs), and ft/s² (US Cust)

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 Vector quantity
 When the sign of the velocity and the acceleration are the same (either
positive or negative), then the speed is increasing
 When the sign of the velocity and the acceleration are in the opposite
directions, the speed is decreasing

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 The limit of the average acceleration as the time interval goes to zero
 When the instantaneous accelerations are always the same, the
acceleration will be uniform
 The instantaneous accelerations will all be equal to the average
acceleration

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 Average acceleration is the slope of the line connecting the initial and
final velocities on a velocitytime graph
 Instantaneous acceleration is the slope of the tangent to the curve of
the velocitytime graph

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 Uniform velocity (shown by red arrows maintaining the same size)
 Acceleration equals zero

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 Velocity and acceleration are in the same direction
 Acceleration is uniform (blue arrows maintain the same length)
 Velocity is increasing (red arrows are getting longer)

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 Acceleration and velocity are in opposite directions
 Acceleration is uniform (blue arrows maintain the same length)
 Velocity is decreasing (red arrows are getting shorter)

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 Used in situations with uniform acceleration

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 Gives displacement as a function of velocity and time

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 Shows velocity as a function of acceleration and time

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 Gives displacement as a function of time, velocity and acceleration

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 Gives velocity as a function of acceleration and displacement

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 Be sure all the units are consistent
 Choose a coordinate system
 Sketch the situation, labeling initial and final points, indicating a
positive direction
 Choose the appropriate kinematic equation
 Check your results

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 All objects moving under the influence of only gravity are said to be in
free fall
 All objects falling near the earth’s surface fall with a constant
acceleration
 Galileo originated our present ideas about free fall from his inclined
planes
 The acceleration is called the acceleration due to gravity, and
indicated by g

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 Symbolized by g
 g = 9.8 m/s²
 g is always directed downward
 toward the center of the earth

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 Initial velocity is zero
 Let up be positive
 Use the kinematic equations
 Generally use y instead of x since vertical

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 a = g
 Initial velocity ¹ 0
 With upward being positive, initial velocity will be negative

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 Initial velocity is upward, so positive
 The instantaneous velocity at the maximum height is zero
 a = g everywhere in the motion
 g is always downward, negative

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 The motion may be symmetrical
 then t_{up} = t_{down}
 then v_{f} = v_{o}
 The motion may not be symmetrical
 Break the motion into various parts

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 Need to divide the motion into segments
 Possibilities include
 Upward and downward portions
 The symmetrical portion back to the release point and then the
nonsymmetrical portion

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