Kinematic Equations Motion with Uniform Acceleration Kinematic Equations

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:

Equation #1 Final Velocity with Constant Acceleration • Start with aavg = v/ t • Rearrange and solve for vf Øvf = 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 Ø 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 Ø vf = 2 2 vi + 2 a( 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 vf 2 = vi 2 + 2 a( 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