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**Motion with Uniform Acceleration**

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 #1 Final Velocity with Constant Acceleration**

Start with aavg = v/t Rearrange and solve for vf vf = vi + a(t) Don’t need to know displacement

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**Equation #2 Displacement 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 Don’t need to know acceleration

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**Equation #3 Displacement 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 Don’t need to know final velocity

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**Equation #4 Final Velocity from Initial Velocity and Acceleration**

vf2 = vi2 + 2a(x) Don’t 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

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Motion in One DimensionSection 2 What do you think? Which of the following cars is accelerating? –A car shortly after a stoplight turns green –A car approaching.

Motion in One DimensionSection 2 What do you think? Which of the following cars is accelerating? –A car shortly after a stoplight turns green –A car approaching.

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