Final answer:
A feasible region is convex if any line segment between two points in the region remains within the region, which is true. In physics, the displacement vs. time graph for an object with constant acceleration is a curve, while displacement vs. time squared is a straight line. Also, vectors in a plane have right angle components, and the amplitude of one wave is not solely affected by another's amplitude, except through superposition.
Step-by-step explanation:
The statement that a feasible region is said to be convex if the line connecting any two points in the feasible region falls entirely within the feasible region is true. This means that if you pick any two points within a convex feasible region and draw a line between them, that line will not exit the boundaries of the region at any point.
Position vs Time Graphs and Vector Components
True or False: Consider an object moving with constant acceleration. The plot of displacement versus time for such motion is a curved line, while the plot of displacement versus time squared is a straight line. The correct answer is true. The displacement vs. time graph for an object under constant acceleration is parabolic, indicating a curve. However, when you plot displacement versus the square of time, the graph becomes a straight line, which confirms uniform acceleration.
True or False: A vector can form the shape of a right angle triangle with its x and y components. The statement is true. Any vector in a two-dimensional space can be broken down into its x (horizontal) and y (vertical) components, forming a right angle triangle.
True or False: The position vs time graph of an object that is speeding up is a straight line is false. If an object is speeding up, the slope of its position vs time graph increases, indicating that the graph will be a curve, not a straight line.
As for the statement on wave amplitude, it's false. The amplitude of one wave is generally not affected by the amplitude of another wave; they can add up or cancel out depending on their relative phases, which is the principle of superposition, but alignment is not the sole requirement.