Question

which of these dot diagrams best describe the motion of a free-falling object that is dropped from rest? tap to select or deselect an answer. diagram a diagram b diagram c

Explanation:

Step1: Recall free - fall motion

A free - falling object (dropped from rest) accelerates due to gravity. The acceleration due to gravity \(g\approx9.8\ m/s^{2}\) means that the velocity of the object increases with time. The distance traveled by the object in successive equal time intervals is given by the equation \(d = v_0t+\frac{1}{2}gt^{2}\), where \(v_0 = 0\) (dropped from rest). So, \(d=\frac{1}{2}gt^{2}\). As time \(t\) increases, the distance \(d\) traveled in each time interval increases. This means that the dots representing the position of the object at equal time intervals should be spaced further and further apart as the object falls (since it is speeding up).

Step2: Analyze the diagrams

• Diagram A: The dots are spaced further apart as we move from left to right (assuming the right - hand side represents later time or lower position in the fall). This is consistent with the object speeding up as it falls, because in each successive time interval, it travels a greater distance.
• Diagram B: The dots are evenly spaced, which would represent an object moving at a constant velocity (uniform motion), not a free - falling object which is accelerating.
• Diagram C: The dots are spaced closer together as we move from left to right, which would represent an object slowing down, which is not the case for a free - falling object dropped from rest.

Answer:

A. Diagram A