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**Velocity and Displacement**

With constant acceleration

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**Another Substitution By combining these two equations:**

With some substitution and algebra, we can get Equation #4 & 5:

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New Equations Now, with two equations, the problem solving process will change slightly…

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Example A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?

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Example A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? Givens: a = 4.8 m/s2 t = 15s vi = 0m/s vf = ? Δx = ? Equations: There is only enough information to use ONE of the equations at first…

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Example A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? Givens: a = 4.8 m/s2 t = 15s vi = 0m/s vf = ? Δx = ? Equations: Solve for vf first…

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Example A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? Givens: a = 4.8 m/s2 t = 15s vi = 0m/s vf = ? Δx = ? Equations:

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Example A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? Givens: a = 4.8 m/s2 t = 15s vi = 0m/s vf = 72m/s Δx = ? Equations:

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Example A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? Givens: a = 4.8 m/s2 t = 15s vi = 0m/s vf = 72m/s Δx = ? Equations: Now solve for Δx:

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Example A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off? Givens: a = 4.8 m/s2 t = 15s vi = 0m/s vf = 72m/s Δx = ? Equations: Now solve for Δx:

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Practice Pg. 55, Practice D

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Kinematic Equations with Constant Acceleration If an object moves with constant acceleration, we can use four kinematics equations Some Assumptions and.

Kinematic Equations with Constant Acceleration If an object moves with constant acceleration, we can use four kinematics equations Some Assumptions and.

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