What is the equation for acceleration?

The primary equation for acceleration is a = Δv / Δt, representing the change in velocity (Δv) divided by the change in time (Δt). This ratio-based definition captures acceleration's essence: how quickly velocity changes, measured in units like meters per second squared (m/s²) or feet per second squared (ft/s²). Written in expanded form, this becomes a = (v_final - v_initial) / (t_final - t_initial), though for problems starting at t = 0, it simplifies to a = (v - u) / t.

This equation serves as the foundation for all other kinematic formulas. Through algebraic manipulation and integration with displacement relationships, it generates the complete set of motion equations physics students memorize. When you see formulas like v = u + at or s = ut + ½at², they're ultimately derived from this core definition combined with the relationships between position, velocity, and time.

In practice, using this equation requires understanding what velocity means in your context. For straight-line motion, velocity is simply speed with a direction (positive or negative). For curved paths, like a car turning at constant speed, acceleration still exists because the velocity vector's direction changes—this is where concepts like centripetal acceleration come into play, using modified versions like a = v²/r. The basic equation a = Δv/Δt remains the conceptual anchor, but the calculation method adapts to the motion's geometry.