Read the changing gaps between positions
Photograph a falling ball at equal time intervals. The gaps between its successive positions grow because the ball gains downward speed. With a calibrated ruler and clock, that changing spacing measures gravitational acceleration: how much downward velocity is added each second.
Near Earth's surface, a small vertical fall in vacuum has an approximately constant acceleration. The same rule applies if the ball is thrown upward. It slows, stops momentarily and falls back; gravity continues acting throughout. Air resistance changes this picture because its force depends on the motion through the air.
Sources: [1]
The release is part of the fit
A release mechanism may give the ball a slight push, and the first camera frame need not coincide with release. Estimating gravity from a single distance and elapsed time can then mix an unknown starting speed with acceleration. Several recorded positions let the initial height, initial velocity and acceleration be fitted together.
The fitted curve is a parabola for constant acceleration. Its starting level sets the height, its initial slope sets the velocity, and its curvature sets gravity. Moving the chosen time origin changes the first two descriptions, but it leaves the curvature unchanged.
The differences between the recorded heights and the curve are called residuals. Random position noise scatters points above and below it. If the noise assumptions hold, many frames can constrain the curvature much more tightly than one pair of positions.
A narrow spread can sit in the wrong place
Repeat the drop with the same setup. The gravity estimates may cluster closely: the measurement is precise. A ruler with an incorrect scale moves the cluster away from the correct value every time. Repeating that calibration error does not average it away.
A fitted standard error describes the spread expected under the fit's assumptions. If the calculation assumes exact times and independent position errors, it does not also cover an inaccurate clock or an unmodeled force. A full uncertainty evaluation includes those contributions and the uncertainty of any corrections.
Drag offers a visible example. During descent it opposes the motion and grows with speed in a linear-drag model. Acceleration then changes during the fall. A parabola may still pass close to a short record, yet its fitted acceleration differs from the gravitational acceleration. Residuals that bend systematically are a reason to examine the physical model.
A photogate times a finite piece of motion
A photogate sends a beam across a gap. An opaque flag interrupts it; timing begins at one edge and ends at the other. Dividing the flag length by the interruption time gives the average speed over that passage. The result refers to a short interval, not a single instantaneous position.
For a calculated example, a ten-centimetre flag that blocks the beam for five milliseconds has an average speed of twenty metres per second. A deliberately coarse fifty-millisecond timer could round that duration to zero. Faster camera sampling cannot recover a time interval that this timer cannot distinguish. These are teaching settings; Vernier's cited photogate specifies microsecond resolution. Actual gates also have an effective optical width that depends on geometry.
Sources: [3]
Make the measuring system part of the question
Absolute gravimeters also use timed falling objects to determine gravity. National Geodetic Survey describes the need for quiet, stable conditions: movement of the instrument can contaminate the motion it is meant to measure. A classroom camera and a precision gravimeter share a basic question even though their instruments and uncertainties differ enormously.
A useful gravity result therefore comes with more than a smooth curve. It explains how distance and time were calibrated, which motion was fitted, and which effects contribute to the uncertainty. The falling body supplies the motion; the measuring system determines how faithfully that motion becomes a number.