Final answer:
To measure the AC/A ratio using the gradient method, plot Distance vs. Time graph, find the gradient to represent average velocity, and use this in centripetal acceleration formulas.
Step-by-step explanation:
To measure the AC/A ratio using the gradient method, start by setting up an experiment to record the centripetal acceleration (ac) of an object moving in a circular path. Record the object's travel distance and the time taken at multiple points to obtain average values for these parameters. Using these averages, plot a Distance vs. Time graph on graph paper. With the graph plotted, you then need to find the gradient of the straight line which will represent the average velocity (v).
After obtaining the average velocity, use the centripetal acceleration formulas (ac = v^2/r where r is the radius) to calculate ac. Lastly, compare the centripetal acceleration (ac) to another suitable measurement, like gravitational acceleration (g), if required for finding the AC/A ratio. The information provided doesn't explicitly describe how to directly measure the AC/A ratio, but rather provides steps to calculate components relevant to the dynamics of circular motion which could contribute to determining such a ratio.