Question

which velocity vs. time graph corresponds to the data represented by the position vs. time graph? position (m) time (s) velocity vs. time

Explanation:

Step1: Analyze Position - Time Graph

The position - time graph is a straight line passing through the origin. The slope of a position - time graph gives the velocity. For a linear position - time graph \(x = vt\) (where \(x\) is position, \(v\) is velocity, and \(t\) is time), the slope \(v=\frac{\Delta x}{\Delta t}\) is constant. So the velocity is constant.

Step2: Determine Velocity - Time Graph

A velocity - time graph for constant velocity should be a horizontal line (since velocity does not change with time). So the corresponding velocity - time graph is a horizontal line (parallel to the time axis) with a non - zero y - intercept (equal to the constant velocity).

Answer:

The velocity - time graph corresponding to the given position - time graph is a horizontal line (indicating constant velocity). If we assume the options for velocity - time graphs are given, the correct one will be a graph where velocity remains constant (a horizontal line) over time.