Kinematic Equations Motion with Uniform Acceleration Kinematic Equations
- Slides: 12
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
Practice Problem #1 • An airplane accelerates down a runway at 3. 20 m/s 2 for 32. 8 s until is finally lifts off the ground. Determine the distance traveled before takeoff.
Practice Problem #2 • A bike accelerates uniformly from rest to a speed of 7. 10 m/s over a distance of 35. 4 m. Determine the acceleration of the bike.
Practice Problem #3 • A car traveling at 22. 4 m/s skids to a stop in 2. 55 s. Determine the skidding distance of the car (assume uniform acceleration).
- Rearranging kinematic equations
- Rotational kinematics
- Kinematic equations for circular motion
- Vfy=viy+gt
- Uniform and non uniform linear motion
- Derive vf^2=vi^2+2ad
- Centripetal acceleration ac
- Relationship between angular and linear quantities
- Radial acceleration formula
- Kinetic angular energy
- Centripetal acceleration tangential acceleration
- Track manager
- Motion along a straight line formulas