Kinematics Formulas: Motion, Speed, and Acceleration
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Kinematics Formulas
Position Vector
r = xi + yj
- x = r cos
- y = r sin
- r = √(x2 + y2)
- tan θ = y / x
Displacement
Δr = r - rinitial
Speed, Average Speed, Instantaneous Speed
- Average Speed: vav = Δr / Δt
- Instantaneous Speed: v = dr / dt
Average Acceleration, Instantaneous Acceleration
- Average Acceleration: aav = Δv / Δt
- Instantaneous Acceleration: a = dv / dt
Uniform Rectilinear Motion (MRU)
- v = Δx / Δt
- vmean = (v0 + v) / 2
- v = v0 + at
- x = x0 + vt
- x = x0 + v0t + (1/2)at2
- v2 - v02 = 2aΔx
- v2 = v02 ± 2as
Free Fall
- Velocity: v = gt
- Position (height fallen): y = (1/2)gt2
- Velocity (upward): v = -gt
- Position (height): y = y0 - (1/2)gt2
Upward Vertical Launch
- Velocity: v = v0 - gt
- Position (height): y = y0 + v0t - (1/2)gt2
- Time to reach maximum height: t = v0 / g
- Maximum