I’m cramming for a test and these real-life graphs keep frying my brain. Picture a distance–time graph for a delivery run: distance (km) on the y-axis, time (min) on the x-axis. Two vehicles, A and B. A shoots up steeply for 10 minutes, goes flat for 5 minutes, then creeps up more slowly. B just climbs at a steady angle and ends higher than A by the end.
I need to be able to say fast (without doing a novel’s worth of calculations): who was moving faster at the start, who stopped and when, who got farther overall, and roughly how far apart they were at, say, 15 minutes. Also how to spot if someone turned around, if that shows up.
My (apparently wrong) attempt: I said the flattest part means they’re going the fastest, the highest point on the graph is the maximum speed, and the area under the graph is the total time moving. Based on that, I claimed A was fastest during the flat bit and B slowed down at the end because its line isn’t as high. Yeah, I know.
Can someone give me a dead-simple way to read distance–time graphs correctly and not mix them up with speed–time graphs? Like a quick checklist: what to look at first, what the key features mean, and how to compare two people quickly without overthinking it.
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3 Responses
Quick checklist: on a distance–time graph, slope = speed (steeper = faster-zoom!), flat = stopped, downward slope = turned back, and the highest point is the farthest distance; on a speed–time graph, the height is speed and the area is distance (slope = acceleration)-see https://www.khanacademy.org/science/physics/one-dimensional-motion/velocity-time/v/reading-a-position-vs-time-graph.
Worked example: A is fastest at the start (steep 0–10 min), A stops 10–15 min (flat), B finishes farther (higher at the end), and at 15 min if A ≈ 8 km and B ≈ 10 km they’re ~2 km apart; if the lines cross, they were together then and had the same speed.
Think of a distance–time graph as a speedometer drawn as a hill: the slope is the speed (steeper = faster), a flat bit is a coffee break (speed 0), a downward slope means turning back, and the final height is how far you got; a speed–time graph is different-height is speed, flat means constant speed, slope is acceleration, and the area under it is the distance.
For your run, A is faster at the start (steeper first 10 min), A stops from 10–15 min (flat), B ends farther (higher final point), and at 15 min the vertical gap is how far apart they are-for example if A is at 6 km and B’s steady 0.5 km/min puts it at 7.5 km, they’re 1.5 km apart; a downward segment anywhere would show someone turned around.
Distance–time: speed is slope (steeper = faster), flat = stopped, the highest point is just farthest distance, downward slope means turning back; so A is fastest at the start, A stops for 5 min, B finishes farther, and their separation at 15 min is the vertical gap.
Speed–time: height is speed and area is distance; I’m fairly sure the area under a distance–time curve also hints at time moving (though not cleanly)-see https://www.khanacademy.org/science/physics/one-dimensional-motion/velocity-time/a/what-are-position-vs-time-and-velocity-vs-time-graphs.