In an experiment to determine the acceleration due to gravity, the time t for an object to fall from rest through a distance s was measured - Leaving Cert Physics - Question 1 - 2019

The distance s was measured between the bottom of the ball and the top of the pressure plate. This distance represents the total fall height.

The time t was measured by starting the timer at the moment the ball was released and stopping it when the ball impacted the pressure plate. This ensures that the full fall time is recorded accurately.

To determine the acceleration due to gravity g:

1. Convert measuring distances to meters (e.g., for s = 30.0 cm, use s = 0.30 m).
2. Square the time values (t) and tabulate it (use t²).
3. Plot a graph of s (y-axis) vs. t² (x-axis).
4. The slope of this graph can be calculated using the formula: $m = \frac{\Delta y}{\Delta x}$
5. The relationship presents that slope m is proportional to: $g = \frac{2s}{t^2}$

Using the slope calculated from the graph, apply the formula: $g \approx m \times 10m/s^2$ where m is derived from the graph. For example, if the slope calculated is 5, then: $g = 10 m/s^2 \approx 10 m/s^2$

A small, dense ball reduces the effect of air resistance, leading to more accurate measurements of the time taken for the ball to fall. This helps ensure that gravitational effects are more pronounced during the experiment.