Lecture 5 PowerPoint - 1 D Motion cont

# Lecture 5 PowerPoint - 1 D Motion cont - Chapter2...

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Motion in One Dimension Chapter 2

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Acceleration and Velocity When an object’s velocity and  acceleration are in the same direction,  the object is speeding up When an object’s velocity and  acceleration are in the opposite  direction, the object is slowing down If velocity is constant, the acceleration  is zero.
CPS Question

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Derivations for Constant  Acceleration For constant acceleration, the average acceleration over any time interval is numerically equal to the instantaneous acceleration over that same time interval. o Therefore, the velocity changes at the same rate throughout the interval dv dt = χονσταντ = α dv = αδτ dv v 0 v = ω - ω 0 = αδτ 0 τ = α δτ 0 τ = α τ - 0 ( 29 = ατ v = ω 0 + ατ
More Derivations v = δξ δτ = ω 0 + ατ dx = ω 0 + ατ ( 29 δτ dx x 0 x = ξ - ξ 0 = ω 0 + ατ ( 29 δτ 0 τ = ω 0 τ + 1 2 ατ 2 x = ξ 0 + ω 0 τ + 1 2 ατ 2

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More Derivations Using the chain rule, we can derive another equation a = δω δτ = δω δξ δξ δτ = ω δω δξ adx = ωδω adx x 0 x = α ( ξ - ξ 0 29 = ωδω ω 0 ω = 1 2 ω 2 - ω 0 2 ( 29 v 2 = ω 0 2 + 2 α ξ - ξ 0 ( 29
For constant acceleration only, The average velocity can be expressed as  the arithmetic mean of the initial and final  velocities 2 xi xf x v v v + = Last Equations x f - ξ ι = ω ξ τ = 1 2 ω ξι + ω ξφ ( 29 τ

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Kinematic Equations for  Constant Acceleration
Freefall The most common constant acceleration is the acceleration that all freely falling bodies experience, the acceleration due to gravity.

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