Kinematic Equations Important Kinematic Equations and their Derivations

Kinematic Equations Important Kinematic Equations and their Derivations

Finding Δx given v and t l We have two equations for average velocity: l l l We can set these equations equal to eachother (Vavg = Vavg) l l Vavg= Δx / Δt Vavg= (vi + vf) / 2 Δx / Δt = (vi + vf) / 2 Now solving for x: l Δx = [(vi + vf) Δt] / 2

Finding vf given a, vi, and t l From our equation for average acceleration: l l a = Δv / Δt = (vf – vi) / Δt We can rearrange to solve for vf: l vf = vi + a • Δt

Finding Δx given vi, a, and t l Using the two equation just derived: l l l Δx = [(vi + vf) Δt] / 2 vf = vi + a • Δt We can sub in for vf and arrive at a new equation for Δx which is not dependent on vf: l l Δx = [(vi + a • Δt) Δt] / 2 Δx = vi • Δt + 1/ 2 • a • (Δt)2

Finding vf given vi, a, and Δx l Using the two equations: l l Δx = [(vi + vf) Δt] / 2 vf = vi + a • Δt l We will derive an equation for vf independent of time l first solve for time from the first equation (we will plug this into the second to get rid of the time variable): l Δt = (2 • Δx) / (vi + vf)

l Now inserting our expression for Δt into the equation vf = vi + a • Δt, we get: l l vf = vi + a • [(2 • Δx) / (vi + vf)] We now need to isolate vf: l l vf – vi = (2 • a • Δx) / (vi + vf)] (vf – vi)(vi + vf)] = 2 • a • Δx vf 2 - vi 2 = 2 • a • Δx vf 2 = vi 2 + 2 • a • Δx (multiply by (vi + vf)) (foil) (get vf by itself)

Useful Kinematic Equations 1. 4. 2. 5. 3. 6.