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3 Responses
Quick idea to keep in mind
– On a distance–time graph, speed is the slope (rise ÷ run), not the height.
– Height tells you “how far from the start by this time,” not “how fast right now.”
– Steeper up = faster forward. Flat = stopped. Downward = going back toward the start.
Why slope means speed
– The y-axis is distance (e.g., km). The x-axis is time (e.g., min).
– Slope = change in distance ÷ change in time, which has units km/min. That’s exactly a speed.
– A higher point on the graph just means “more total distance covered so far,” which is different from “speed at that moment.”
How to draw your trip (2 km in 10 min, then rest until 20 min)
1) Axes: put time (minutes) on the horizontal axis from 0 to 20, and distance (km) on the vertical axis from 0 to at least 2.
2) Start at (0, 0).
3) Moving segment: draw a straight line from (0, 0) to (10, 2). That’s a constant slope, so a constant speed.
– Speed on this segment = slope = 2 km ÷ 10 min = 0.2 km/min = 12 km/h.
4) Rest segment: from (10, 2) to (20, 2) draw a horizontal line. That’s zero slope, so speed = 0.
How to read speed quickly (no-nonsense rules)
– Pick a small time window around the moment you care about.
– Draw a little right triangle under the graph there.
– Rise = how much distance changes in that window.
– Run = how much time passes in that window.
– Speed = rise ÷ run.
– Steeper line (bigger rise for the same run) = faster.
– Flat line (rise = 0) = stopped.
– If two people have graphs at the same time, the one with the steeper slope at that time is moving faster, even if their line is lower on the page.
Worked example (including your scenario)
– From 0 to 10 min: line from (0, 0) to (10, 2).
– Speed = 2/10 = 0.2 km/min = 12 km/h.
– From 10 to 20 min: horizontal at 2 km.
– Speed = 0 km/min = 0 km/h.
– Average speed over the whole 20 min: total distance ÷ total time = 2 km ÷ 20 min = 0.1 km/min = 6 km/h.
– You can see this by drawing a straight line from (0, 0) to (20, 2): its slope is the average speed.
A tiny “higher vs. steeper” contrast
– Suppose at t = 10 min:
– Person A is at 2.0 km and their graph is flat (slope 0) – they’re stopped.
– Person B is at 1.2 km but their graph is quite steep, say slope 0.3 km/min (18 km/h).
– Even though A’s point is higher (farther from the start), B is moving faster right now because B’s slope is steeper.
Handy mnemonic
– Speed = Slope. Stop = flat. Steeper = speedier.
Further reading
– Clear visuals and examples: “Distance-Time Graphs” on Math is Fun: https://www.mathsisfun.com/graphs/distance-time-graphs.html
– (If you like physics-style explanations) Khan Academy on position–time graphs: https://www.khanacademy.org/science/physics/one-dimensional-motion/position-time-graphs/a/what-are-position-time-graphs
On a distance–time graph, speed is the slope: steeper = faster; for 2 km in 10 min draw (0,0)→(10,2) and then a horizontal line to 20 min, with speed 2/10 = 0.2 km/min. The point’s height at 10 min is that speed up to then, so a higher line there means faster. Hope this helps!
Speed on a distance–time graph is the slope: steeper tilt = faster, flat = stopped; the height only shows how much distance you’ve accumulated, not how fast you’re moving right then. For your trip, draw from (0,0) to (10,2) (speed 2 km/10 min = 0.2 km/min = 12 km/h), then a horizontal line from (10,2) to (20,2)-think of the tilt like a speedometer needle: tilted up means zooming, level means parked.