Kinematic Equations
Motion with Uniform Acceleration
Kinematic Equations
• Relationships between displacement,
velocity, acceleration, and time
• Only work when acceleration is
uniform (constant)!!
Kinematic Equations
All equations
derived from three
relationships that
you already know:
vavg
v f  vi

2
aavg
vavg
x

t
v

t
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
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
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
2
a(t)
– Don’t need to know final velocity
Equation #4
Final Velocity from Initial Velocity and
Acceleration
2
vf
=
2
vi
+ 2a(x)
– Don’t need to know time
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)


Solving Problems Using Kinematic
Equations
1. Determine what the question is asking
for
2. List all known quantities
– Remember, each equation contains four
variables, so you need to know three
variables in order to solve for the fourth
3. Pick the appropriate equation
4. Solve for desired quantity