# Motion with Uniform Acceleration

## Presentation on theme: "Motion with Uniform Acceleration"— Presentation transcript:

Motion with Uniform Acceleration
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 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 a(t)2 Don’t need to know final velocity

Equation #4 Final Velocity from Initial Velocity and Acceleration
vf2 = vi2 + 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
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