Final answer:
The statement is false; the direction of the velocity vector is dependent upon the direction of movement, while acceleration (not velocity) indicates speeding up or slowing down.
Step-by-step explanation:
The direction of the velocity vector is indeed dependent upon the direction the object is moving; however, whether the object is speeding up or slowing down does not directly affect the direction of the velocity vector, but rather the direction of the acceleration vector. Therefore, the statement is false. Velocity is a vector quantity with both magnitude and direction, and the velocity's direction is solely the direction in which the object is moving. On the other hand, acceleration, which is also a vector, indicates whether an object is speeding up or slowing down. If acceleration is in the same direction as the object's motion, the object speeds up; if it's in the opposite direction, the object slows down.
An example of this would be a car moving forward (positive velocity) but braking (negative acceleration). The velocity vector direction remains in the forward direction, while the acceleration vector points backward, indicating slowing down.
Focusing on graphical representations, the position vs time graph of an object that is speeding up is not a straight line; it is curved, indicating a change in slope (and therefore velocity), so the correct answer is false. Furthermore, consider an object moving with constant acceleration; the plot of displacement (not displacement squared) versus time for such motion is a curved line, representing the change in velocity over time. This makes the previous statement also false.