Answer :

Final answer:

The provided true or false statements about physical displacement, graph representation of motion, vector components, the Louisiana Purchase, Dillon's Rule, and the Pythagorean theorem involve principles of physics and history. Most of the statements provided are false except for two which are true.

Explanation:

Displacement of Two Persons: The statement is False. Displacement is a vector quantity that has both magnitude and direction. It is independent of the path taken; thus, both persons have the same displacement since they end up at the same point relative to the starting position, regardless of the order of movements.

Position vs Time Graph: The statement is False. The position vs time graph for an object speeding up is not a straight line but a curve that gets steeper over time, indicating increasing speed.

Vector and Right-Angle Triangle: This statement is True. A vector can be represented as the hypotenuse of a right-angle triangle with its x and y components representing the adjacent and opposite sides, respectively.

Louisiana Purchase: The statement is True. The Louisiana Purchase approximately doubled the territory of the United States.

Dillon's Rule: The statement is False. Dillon's Rule limits the powers of local government to only those expressly granted by state law or those powers closely linked to the express powers.

Using Pythagorean Theorem on Vectors: The statement is True. If two vectors are at right angles, you can use the Pythagorean theorem to calculate the magnitude of the resultant vector.

Constant Speed: A car moving on a straight road at a constant speed in a single direction maintains the same velocity, which means its acceleration is zero.

Displacement and Acceleration Graphs: The statement is True. For constant acceleration, a displacement vs time graph shows a curved line, whereas a displacement vs time squared graph shows a straight line.

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