Question

A graph with no grid lines or values titled Position versus Time, shows shows time in seconds on the x axis, and position in meters on the y axis.There are three lines on the graph labeled A, B, and C. All three lines start in the bottom left and point to the top right. Lines A and B both start at the origin with line A steeper. Line C is not as steep as A and B and starts on the y axis further up than the origin and it crosses both lines A and B ending higher than either.
Using the information in the graph, compare the motion of runners A, B, and C. Be sure to compare the initial position and velocity of each runner.

Answer 1

Key facts to read from a position vs time graph:
- The y-intercept is the runner's initial position (position at t = 0).
- The slope of the line is the runner's velocity (steeper = larger speed, positive slope = moving forward).

What the graph tells us:
- Initial positions: A and B both start at the origin (x = 0), so their initial position is 0 m. C starts higher on the y–axis, so C’s initial position is greater than 0 m (C is ahead at t = 0).
- Velocities: A’s line is steeper than B’s, so A has a greater velocity than B (vA > vB). Because C crosses both A and B and finishes highest, C must have the largest slope (velocity) of the three, so vC > vA > vB.
- Overall motion: All three runners move forward (all slopes are positive). C starts ahead and, having the greatest speed, increases its lead and ends farther ahead. A is faster than B, so A moves ahead of B (and A may or may not overtake C depending on exact slopes, but given C ends highest, C remains ahead of A and B).

Note: if the graph truly shows C “not as steep” as A and B but still crossing and ending higher, that would be inconsistent — a line with a smaller slope cannot overtake and finish above lines with larger slopes unless the lines are not straight or the description is mistaken. If you can confirm the slopes visually, I can restate the comparisons precisely.