What acceleration really means
Acceleration is the rate at which velocity changes — and because velocity is a vector, so is acceleration. Its SI unit is metres per second, per second (\text{m/s}^2): an acceleration of 3\text{ m/s}^2 means the velocity grows by 3 m/s during every second.
Average acceleration is the change in velocity over the elapsed time; instantaneous acceleration is its limit — the derivative of velocity, or the slope of the velocity–time graph.
Seeing acceleration in a motion diagram
Acceleration is where the motion diagram earns its keep. If the strobe dots grow steadily farther apart, the velocity is increasing at a steady rate — that is constant acceleration, the single most important special case in introductory physics because it describes a car pulling away, a puck sliding to a stop, and every object falling near the Earth.
The four equations of constant-acceleration motion
When acceleration a is constant, the whole motion is captured by the constant-acceleration equations. They link five quantities — initial velocity v_0, final velocity v, acceleration a, displacement x - x_0, and time t — so that if you know three of them you can always find the rest.
Velocity grows linearly in time (no displacement here). This is just the definition of constant acceleration rearranged.
Displacement in terms of time. The ½at² term is the extra ground covered because the velocity is changing.
The time-free equation — perfect when a problem never mentions time (e.g. 'how far to stop?').
Free fall: gravity as constant acceleration
The most famous constant acceleration of all is gravity. In free fall — motion under gravity alone — every object near the Earth's surface accelerates downward at g ≈ 9.8 m/s², regardless of its mass. A feather and a hammer really do fall together, as Galileo argued and the Apollo 15 astronauts demonstrated on the airless Moon.
The constant-acceleration equations with a = −g (taking up as positive). Gravity does the same job here as any other constant acceleration.