Motion in One Dimension — Cheat Sheet (Page 1)

Vocabulary flashcards covering symbols, units, key kinematics formulas, and the quick-select flowchart for one-dimensional motion.

d (Distance / Displacement)

Distance or displacement; units: meters (m) or kilometers (km).

v (Velocity / Speed)

Rate of motion; units: meters per second (m/s) or kilometers per hour (km/h).

v_i (Initial Velocity)

Velocity at the start of motion.

v_f (Final Velocity)

Velocity at the end of motion.

a (Acceleration)

Rate of change of velocity; units: m/s^2.

t (Time)

Elapsed time; units: seconds (s).

g (Gravity)

Acceleration due to gravity; approximately 9.8 m/s^2.

v = d / t

Average speed with no acceleration.

a = (vf - vi) / t

Acceleration from velocity change.

d = v_i t + 1/2 a t^2

Distance traveled under constant acceleration.

vf = vi + a t

Final velocity after acceleration over time t.

vf^2 = vi^2 + 2 a d

Final velocity squared equals initial velocity squared plus 2ad (use when time is not given).

d = 1/2 g t^2

Free fall distance; assumes v_f = 0.

vavg = (di + df) / (ti + t_f)

Average speed for two-speed/two-time segments.

ttop = vf / g

Time to reach the maximum height in a vertical rise.

ttotal = 2 × ttop

Total flight time for a projectile that lands at the same height.

Flowchart Step 1: Acceleration check

If there is no acceleration, use v = d / t; otherwise proceed to Step 2.

Flowchart Step 2a: Time given?

If time is given, use vf = vi + a t or d = v_i t + 1/2 a t^2.

Flowchart Step 2b: Time not given?

If time is not given, use vf^2 = vi^2 + 2 a d.

Flowchart Step 3: Free fall?

Set a = g = 9.8 m/s^2.