Final answer:
It is true that a vector can form a right-angle triangle with its components. The statement about displacement being the same regardless of the path taken is false, as is the notion that a position vs time graph for an accelerating object is straight. It is also true that the displacement vs time graph is curved for constant acceleration, and displacement vs time squared is a straight line.
Step-by-step explanation:
When dealing with vectors in physics, it is true that a vector can form the shape of a right-angle triangle with its x and y components. This is because vectors can be broken down into perpendicular components that align with the x and y axes of a coordinate system, which can then form the legs of a right-angle triangle, with the vector itself representing the hypotenuse. As for the statement that displacement will be the same regardless of whether directions are followed correctly, this is false. Displacement is a vector quantity that depends on the starting and ending points, so taking a different path can lead to a different displacement.
The position vs time graph of an object that is speeding up is not a straight line, so that statement is false. Such a graph would show a curve that gets steeper over time as the speed increases.
Lastly, when considering an object moving with constant acceleration, the plot of displacement versus time is indeed a curved line, which is true. However, if we plot displacement vs the square of time, we'll get a straight line, confirming that the object has constant acceleration.