Final answer:
A student can find the acceleration of an object in free fall by plotting its displacement against the square of the time it takes to fall. The slope of this graph, when doubled, gives the acceleration due to gravity, as long as air resistance is negligible.
Step-by-step explanation:
The student can determine the acceleration of the object in free fall by analyzing the graph of displacement versus time squared. In the case of an object released from rest and in free fall under the influence of gravity, the relationship between the displacement (y) and the squared time (t^2) is given by the kinematics equation for uniformly accelerated motion: y = (1/2)gt^2, where g is the acceleration due to gravity.
By plotting displacement y on the y-axis against time squared t^2 on the x-axis, the graph obtained should be a straight line. The slope of this line represents (1/2)g. Therefore, the student can determine the acceleration due to gravity (g) by finding the slope of the line and multiplying by 2.
If we assume that the acceleration due to gravity g is 9.81 m/s^2, the slope of the line will yield a value close to this, as long as air resistance is negligible. Since the slope is constant, it reinforces that the acceleration is also constant during the object's free fall.
This method of using motion detector data to graph displacement against time squared provides a hands-on approach for students to understand the concept of constant acceleration due to gravity and apply kinematics equations to predict motion.