Given a velocity-time graph, which type of position-time graph would correspond to a constant velocity?

A velocity-time graph that represents constant velocity is characterized by a horizontal line, indicating that the velocity does not change over time. When the velocity is constant, the object moves at the same speed in the same direction without any acceleration.

In terms of position-time graphs, a constant velocity leads to a linear relationship between position and time. This means that the position changes at a steady rate, resulting in a graph that is a straight line with a constant slope. If the velocity is positive, the line will slant upwards; if the velocity is negative, it will slant downwards.

Given the options, a horizontal line directly represents zero velocity on the velocity-time graph; on a position-time graph, a linear relationship corresponds to both continued movement (constant velocity) and the uniform nature of that movement. Therefore, while a gradual slope indicates decreasing speed over time, it does not accurately portray constant velocity. A steep slope would indicate a higher constant velocity, while a curved line would imply changing velocity.

Thus, the correct representation of a position-time graph corresponding to a constant velocity would logically manifest as a straight line, reflecting unchanging speed.