The graph shows a moored rowboat's position relative to a dock marker. Which way is the boat moving during segment F?
A hiker walks a straight trail at a steady 2 m/s, never stopping, never turning back. The trail crosses a small footbridge about 6 m from the trailhead.
A classmate sketches a position-time graph of the hike for the trail guide. Here is the sketch.
The classmate's sketch. The bump in the middle is a little copy of the footbridge.
On a position-time graph, every stretch of the line is a claim about the motion. What does the bump claim?
From 4 s to 5 s the bump's right side falls, from 9 m down to 6 m. On this graph, that says the hiker walked 3 m backward. She only ever walked forward.
A position-time graph plots position against time. It is not a map of the path. So a bridge or a hill on the trail does not put a bump in the graph.
Her real hike: a steady 2 m/s, never stopping, never turning. One straight rising segment, footbridge or not.
Another offer, another flaw: a vertical jump claims the hiker covered 4 m with no time passing. No motion can do that.
To evaluate an offered graph, check the description against the graph one segment at a time: each stage of the motion must match the shape of its segment. To report a flaw, name the segment and the claim it breaks.
Try it yourself. A robot vacuum drives 6 m in the positive direction in 3 s, pauses for 2 s, then drives back to its start in 3 s. The graph below is offered for this motion.
The offered graph.
What is the flaw? Check each stage against the description before you continue.
The rise to 6 m in 3 s matches the drive out. The flat segment from t = 3 s to 5 s matches the pause. Then, at t = 5 s, the graph drops from 6 m to 0 m with no width along the time axis: a vertical jump. The description gives the drive back 3 s; the jump gives it no time at all. The flaw is the vertical drop at t = 5 s.
A student walks 4 m in the positive direction in 4 s, stands still for 2 s, then walks 4 m farther in the positive direction in 4 s. The graph shown is offered for the walk. What is the flaw?
One more. A jogger runs in the negative direction at a steady pace for 5 s, starting from the door of a gym. The graph below is offered for the run.
The offered graph.
What is the flaw this time?
The description says the jogger runs in the negative direction. The offered segment rises, so its slope is positive. The slope of a position-time graph at a moment is the velocity at that moment, sign included, so a rising segment claims positive-direction motion. The flaw is the rising segment: the jogger's positions should fall as time passes, not rise.
A remote-control car drives at a steady speed along a straight track that dips through a shallow trench. Position is measured as distance traveled along the track. The graph shown is offered for the drive. What is the flaw?
A swimmer starts 12 m from the pool's zero mark, on the positive side, and swims in the negative direction at a steady pace for 3 s, then rests for 3 s. The graph shown is offered for the swim. What is the flaw?
Your turn
A runner moves in the positive direction at a steady pace for 6 s. The graph shown is offered for the run. What is the flaw?
A car drives at a steady speed along a straight road that climbs a hill and comes down the other side. Position is measured as distance traveled along the road. The graph shown is offered for the drive. What is the flaw?
A walker goes 6 m in the positive direction in 3 s, stands still for 3 s, then goes 6 m farther in 2 s, walking faster than before. The graph shown is offered for the walk. What is the flaw?