Final answer:
The position vs. time graph for a free-falling object is curved because its velocity increases at a steady rate due to constant acceleration from gravity, represented by a steeper slope on the graph over time.
Step-by-step explanation:
The position vs. time graph for an object in free fall is a curve because of the constant acceleration due to gravity. As the object falls, its velocity increases at a steady rate, meaning the slope of the position vs. time graph, which represents velocity, gets steeper as time progresses. This acceleration causes the graph to curve upwards when the object is moving downwards towards the ground. In a free-falling object’s motion, the position changes with the square of time due to the constant acceleration imparted by gravity.
When we look at the slope of the position vs. time graph at any point, we are looking at the object's instantaneous velocity. If we drew tangent lines to the curve at various points in time, the slope of these lines would represent the velocity at those points. As gravity pulls the object downwards, the velocity increases over time, which is depicted as a steeper slope on the graph. The continuously changing slope results in a curved line on the position versus time graph, showing that velocity is not constant but increasing due to the influence of gravity.