How acceleration works
Acceleration is the rate of change of velocity. For constant acceleration over a time interval:
a = (v₁ − v₀) ÷ t · d = (v₀ + v₁) ÷ 2 × t
The displacement formula works because velocity changes linearly in time, so its average over the interval is simply the mean of the endpoints, (v₀ + v₁)/2. The third standard form, v² = v₀² + 2ad, eliminates time entirely and is what you use when you know a velocity and a distance but not how long it took.
Worked example
A car accelerates from rest (v₀ = 0) to 25 m/s in 10 s: a = (25 − 0) ÷ 10 = 2.5 m/s², and it covers d = (0 + 25)/2 × 10 = 125 m. Note how a 0–100 km/h time is just this calculation with unit conversion: 27.8 m/s in about 9 s is roughly 3.1 m/s², which is why cars are often quoted with an "acceleration figure in units of 0–60 mph".
Sign, gravity and everyday feel
The sign of a tells you the story: positive means velocity is increasing in the chosen positive direction, negative means slowing down (or accelerating the other way), zero means constant velocity — and note that constant velocity means zero acceleration, not "no forces acting". Near Earth's surface gravity gives about 9.81 m/s² downward, so anything falling without air resistance gains 9.81 m/s of speed every second, reaching 98.1 m/s after 10 s and falling about 490 m. With air resistance, the object instead approaches a lower terminal velocity — which is why a skydiver stops accelerating and a thrown ball does not.