Final answer:
Understanding the relationship between displacement, velocity, and acceleration is crucial when interpreting graphs. The acceleration of an object can be determined by the slope of a velocity vs. time graph, and for constant acceleration, displacement vs. time squared yields a straight line.
Step-by-step explanation:
For true or false questions related to graph interpretation, it is crucial to understand basic calculus and physics concepts, such as the relationship between position, velocity, and acceleration in the context of functions and their derivatives.
Velocity vs. Time Graph
The statement that taking the slope at any point on the velocity vs. time graph gives the jet car's acceleration is true, provided that the graph is linear, which indicates a constant acceleration. If the graph has a constant slope of 5.0 m/s², then the jet car's acceleration is indeed 5.0 m/s².
Velocity at a Specific Time
The velocity of the jet car at t = 20 s can be verified by reading the value directly from the graph, so the statement about taking the slope to find the velocity is false. To verify the velocity, one should reference the value on the velocity axis that corresponds to t = 20 s, not the slope.
Position vs. Time Graph
For an object moving with constant acceleration, a plot of displacement versus time is a parabolic curve, not a straight line. Hence the statement is false. However, when plotting displacement versus the square of time, the graph becomes a straight line, confirming that the acceleration is constant.
The statement that the position vs time graph of an object that is speeding up is a straight line is false; the correct statement is that the position vs time graph of an object that is speeding up is a curve that gets steeper over time.
Regarding the function f(x) that is a horizontal line between 0 ≤ x ≤ 20, this statement holds true as the value of f(x) does not change within the specified domain.