1. Velocity and Displacement
With constant acceleration

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

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

4. 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?

5. 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…

6. 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…

7. 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:

8. 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:

9. 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:

10. 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:

11. Practice
Pg. 55, Practice D