What is the formula for acceleration? I've heard it's a=2d/t² but I'm confused.

The formula a = 2d / t² is a specific case of acceleration calculation that applies only when an object starts from rest (initial velocity = 0). It's derived from the more general kinematic equation d = ut + ½at², which simplifies to d = ½at² when u = 0, then rearranged to solve for a. This limited applicability is why confusion arises—many sources present it as "the" acceleration formula when it's actually one specialized version among several.

The truly universal definition of acceleration is a = Δv / Δt (change in velocity over change in time), which works regardless of initial conditions. If a skateboard goes from 3 m/s to 9 m/s in 2 seconds, a = (9-3)/2 = 3 m/s²—no need to consider distance or whether it started from rest. The 2d/t² formula would give an incorrect answer here because it assumes zero initial velocity, producing a = 2d/4 that doesn't account for the skateboard's existing motion.

Understanding when each formula applies prevents calculation errors. Use a = 2s/t² for objects dropped from rest, projectiles at the start of launch, or vehicles accelerating from a standstill when you only measured distance and time. For everything else—objects already in motion, deceleration scenarios, or when you have velocity data—stick with a = (v-u)/t or a = (v²-u²)/2s. The difference between these formulas isn't just mathematical; it reflects different physical situations that demand different analytical tools.