Graphs
Comprehensive notes, formulas, and practice questions for Graphs.
Graphs
Distance–Time Graphs
What you'll learn
- Plotting distance on y-axis and time on x-axis to visualise motion.
- Straight line through origin → uniform motion; slope = speed.
- Steeper slope → higher speed; horizontal line → object at rest.
- Reading graphs to compare two athletes or vehicles.
- NCERT graph paper exercises for school track data.
- Interpreting curved lines as non-uniform (acceleration — intro only).
Key concepts
Level 1 — Core idea
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Distance-time graph — each point (t, d) shows position at that instant.
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Slope — rise/run = Δd/Δt = speed (for uniform motion).
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Horizontal portion — distance unchanged → object stationary.
Level 2 — Process and representation
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Diagram (text) — line from (0,0) to (5 s, 25 m): slope = 25/5 = 5 m/s.
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Comparing graphs — steeper line = faster object.
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Non-uniform — curved graph; slope changes at each point.
Level 3 — Applications and NCERT links
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NCERT Activity — plot data from walking 10 m every 2 s; verify straight line.
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Real world — GPS apps plot distance vs time on trips.
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Units on axes — always label metres (m) and seconds (s).
Worked example
Plotting and interpreting a distance-time graph for a walker
Data: time (s): 0, 2, 4, 6, 8; distance (m): 0, 6, 12, 12, 18.
Step 1 — Draw axes: x = time (s), y = distance (m); choose scale 1 cm = 2 s and 1 cm = 4 m.
Step 2 — Plot points (0,0), (2,6), (4,12), (6,12), (8,18).
Step 3 — Join with straight segments.
Step 4 — Segment 0–4 s: slope = 12/4 = 3 m/s (uniform walking).
Step 5 — Segment 4–6 s: horizontal → rest for 2 s (distance stays 12 m).
Step 6 — Segment 6–8 s: slope = (18−12)/(8−6) = 6/2 = 3 m/s (walking again).
Step 7 — Total distance = 18 m; total time = 8 s; average speed = 18/8 = 2.25 m/s.
Conclusion: graph shows motion, rest, and motion again; slope gives speed.
Common mistakes
| Misconception | What students think | Scientific correction |
|---|---|---|
| Plotting time on y-axis and distance on x-axis (wro | Plotting time on y-axis and distance on x-axis (wrong convention for NCERT). | Check the Key concepts and worked example for the NCERT-accurate version. |
| Calculating slope without matching units on both ax | Calculating slope without matching units on both axes. | Check the Key concepts and worked example for the NCERT-accurate version. |
| Joining points with curves when motion between points w | Joining points with curves when motion between points was uniform (use straight segments). | Check the Key concepts and worked example for the NCERT-accurate version. |
| Confusing distance-time graph with speed-time g | Confusing distance-time graph with speed-time graph. | Check the Key concepts and worked example for the NCERT-accurate version. |
| Saying steeper line means slower motion. | Saying steeper line means slower motion. | Check the Key concepts and worked example for the NCERT-accurate version. |
| Confusing steepness with total distance. | Confusing steepness with total distance. | Check the Key concepts and worked example for the NCERT-accurate version. |
Quick check
- What does the slope of a distance-time graph represent?
- How does the graph look for an object at rest?
- Two lines: one slope 2 m/s, one 5 m/s — which is faster?
- What does a horizontal segment on the graph mean?
- From a graph, distance 40 m at 10 s — find speed.
- Draw sketch of distance-time graph for uniform motion.
Open the Practice tab for graded questions on Distance–Time Graphs.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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