Question

vectors quick check
which statement is true regarding a distance vs. time graph? (1 point)

the graph must have a horizontal segment.
the graph can include only straight line segments.
the graph needs to start at the origin.
the graph should show distance on the vertical axis.

Explanation:

1. Analyze "The graph must have a horizontal segment": A distance - time graph doesn't have to have a horizontal segment. For example, an object moving at a constant non - zero velocity will have a non - horizontal (sloped) line, and an object with changing velocity can have a curved line or a series of sloped lines without a horizontal part. So this statement is false.
2. Analyze "The graph can include only straight line segments": A distance - time graph can have curved segments. For instance, if an object is accelerating, the distance - time graph will be a curve (since distance $d=v_0t+\frac{1}{2}at^2$ for uniformly accelerated motion, which is a quadratic function and its graph is a parabola). So this statement is false.
3. Analyze "The graph needs to start at the origin": The graph does not need to start at the origin. If an object already has a non - zero distance from the reference point at time $t = 0$, the graph will start at a point above the origin on the distance axis. For example, if a car is already 5 meters away from a starting line at time $t = 0$, the distance - time graph will start at $(0,5)$ instead of the origin. So this statement is false.
4. Analyze "The graph should show distance on the vertical axis": In a distance - time graph, by convention, the independent variable (time) is on the horizontal (x - axis) and the dependent variable (distance, which depends on time) is on the vertical (y - axis). So this statement is true.

Answer:

The graph should show distance on the vertical axis.