Final answer:
The statement about the absolute value function is false because a negative "a" means the graph opens down. The position vs time graph of a speeding object is curved, not straight. Vectors for negative and positive accelerations point in opposite directions, and a vector can form a right angle triangle with x and y components.
Step-by-step explanation:
The statement that "In the vertex form of an absolute value function, if "a" is negative, the graph opens up" is False. In fact, when dealing with absolute value functions, the value of "a" indicates the direction in which the graph opens. If "a" is positive, the graph opens up, and if "a" is negative, the graph opens down.
Looking at other questions related to the motions of objects and the interpretation of graphs:
- The position vs time graph of an object that is speeding up is not necessarily a straight line. If an object is accelerating, its position vs time graph will be curved, indicating a change in velocity over time. Therefore, statement 18 is False.
- The vector for negative acceleration does indeed point in the opposite direction to the vector for positive acceleration, which means that statement 21 is True.
- A vector can certainly form the shape of a right angle triangle with its x and y components, making statement 60 True.
- Changes in the slope of a line represent changes in the steepness of the line, independent of whether the slope is positive or negative.
Exploring the concept of slopes further:
- A line with a positive slope (b > 0) slopes upward to the right.
- A line with a slope of zero (b = 0) is a horizontal line.
- A line with a negative slope (b < 0) slopes downward to the right.
Graphical interpretations of a line's slope have practical implications when analyzing motion in physics.