# Velocity and Displacement

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Velocity and Displacement
With constant acceleration

Another Substitution By combining these two equations:
With some substitution and algebra, we can get Equation #4 & 5:

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

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?

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…

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…

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:

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:

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:

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:

Practice Pg. 55, Practice D