Final answer:
The vertical position vs. time graph for projectile motion or free fall depicts a parabolic shape, reflecting the nonlinear change of vertical position over time due to gravity's constant acceleration. It represents only the vertical component of motion, with the peak indicating a velocity of zero.
Step-by-step explanation:
The graph of vertical position versus time in projectile motion or during free fall shows the vertical position of an object as it moves under the influence of gravity. This graph is parabolic, reflecting that the vertical position changes nonlinearly over time. Initially, if an object is thrown upwards, its vertical position increases, slows down at the peak, and then decreases as it comes back down. It's important to note that this graph represents only the vertical component of motion. For an object thrown vertically upwards, at its highest point, the vertical velocity is zero, then it starts to increase in the opposite direction (downwards) as it falls back to the ground. Due to gravity's constant acceleration, the object's vertical position changes with time in a parabolic shape. The misconception is that the graph may suggest horizontal motion due to its shape; however, the horizontal axis is time, not space. The actual path of the object is a vertical line when viewed from its side. The independence of vertical and horizontal motions should be recognized when analyzing projectile motion, as shown in figures where vertical and horizontal velocities are treated separately.