Final answer:
The term 'stationary design line' is likely out of context for physics, but the provided statements about physical concepts such as the position vs time graph, standing waves, vector components, and object stability can be addressed as false and true accordingly.
Step-by-step explanation:
A stationary design line in the context of hair cutting refers to a guideline that does not move and to which all hair is directed to be cut at the same length. However, the question appears to be related to Physics, as the subsequent parts address topics like position vs time graphs, standing waves, vector components, and the stability of objects, which are common concepts in Physics coursework. Therefore, the answer to the question "A stationary design line is a guide to where all lengths are directed and is stable?" is not related to Physics and seems to be a misplaced statement. Instead, we should address the true or false statements provided which pertain to physical concepts.
The position vs time graph of an object that is speeding up is not a straight line but a curve that increases in steepness, so the answer is False.
A standing wave is not two identical waves propagating in the same direction; instead, it is the result of two identical waves traveling in opposite directions and interfering with each other. The correct answer is False.
For a vector to form the shape of a right angle triangle with its x and y components, it must have both a horizontal and vertical component, which is possible, so the answer is True.
Considering an object moving with constant acceleration, the plot of displacement versus time would indeed be a curved line, and the plot of displacement versus time squared would be a straight line, so the answer is True.
Regarding equilibrium, a round pencil lying on its side is in neutral equilibrium when displaced perpendicular to its length, but may roll if displaced parallel to its length, indicating unstable equilibrium in that direction. Suspension bridge towers provide high levels of stable equilibrium necessary to support the bridge's deck and the loads it carries.