1. Motion with Uniform Acceleration
Kinematic Equations
Motion with Uniform Acceleration

2. Kinematic Equations
Relationships between displacement, velocity, acceleration, and time
Only work when acceleration is uniform (constant)!!

3. Kinematic Equations
All equations derived from three relationships that you already know:

4. 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

5. 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

6. 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

7. Equation #4 Final Velocity from Initial Velocity and Acceleration
vf2 = vi2 + 2a(x)
Don’t need to know time

8. 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)

9. 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