Kinematic Equations

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Kinematic Equations

• Motion with Uniform Acceleration

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Kinematic Equations

• Relationships between displacement, velocity,
  acceleration, and time
• Only work when acceleration is uniform
  (constant)!!

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Kinematic Equations
All equations derived from three relationships that you already know
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Equation 1Final Velocity with Constant
Acceleration

• Start with aavg ?v/?t
• Rearrange and solve for vf
• vf vi a(?t)
• Dont need to know displacement

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Equation 2Displacement knowing Change in
Velocity

• Start with the two equations for vavg
• Set them equal to each other
• Solve for ?x
• ?x ½ (vi vf)?t
• Dont need to know acceleration

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Equation 3Displacement from Initial Velocity
and Acceleration

• Start with first two kinematic equations
• Substitute expression for vf from 1 into
  equation 2
• Simplify and solve for ?x
• ?x vi(?t) ½ a(?t)2
• Dont need to know final velocity

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Equation 4Final Velocity from Initial Velocity
and Acceleration

• vf2 vi2 2a(?x)
• Dont need to know time

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Equation vf vi a ?x ?t
?x ½ (vi vf)?t ? ? ? ?
vf vi a(?t) ? ? ? ?
?x vi(?t) ½ a(?t)2 ? ? ? ?
vf2 vi2 2a(?x) ? ? ? ?
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Solving Problems Using Kinematic Equations

• Determine what the question is asking for
• List all known quantities
• Remember, each equation contains four variables,
  so you need to know three variables in order to
  solve for the fourth
• Pick the appropriate equation
• Solve for desired quantity