Summary: Speed Distance And Time

Table of Contents
1. Distance-Speed-Time Relation
2. Unit Conversion (km/h ↔ m/s)
3. Average Speed
4. Relative Speed
5. Trains, Overtaking and Crossing
6. Boats and Streams
7. Distance-Time and Speed-Time Graphs
8. Exam Tips and Shortcuts
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Distance-Speed-Time Relation

Core formulas and direct definitions used in all problems.

• Basic relation: D = S × T; hence S = D/T, T = D/S.
• Uniform motion: speed is constant; distance is proportional to time.
• Unit care: ensure D, S, T are in compatible units before using formulas.

Unit Conversion (km/h ↔ m/s)

• Convert km/h to m/s: multiply by 5/18; e.g., 18 km/h = 5 m/s.
• Convert m/s to km/h: multiply by 18/5; e.g., 10 m/s = 36 km/h.
• Shortcut: convert time to hours when speed in km/h, to seconds when using m/s.

Average Speed

• Definition: Average speed = total distance / total time.
• Equal times: average = (a + b)/2 for two speeds a, b.
• Equal distances (two speeds): average = (2×a×b)/(a + b) (harmonic mean).
• Multi-segment: compute total distance and total time, then divide - do not average speeds directly.

Relative Speed

• Opposite directions: relative speed = S₁ + S₂; use for meeting problems.
• Same direction: relative speed = |S₁ - S₂|; use for overtaking/catching up.
• Units: convert both speeds to same unit (m/s or km/h) before adding/subtracting.

Trains, Overtaking and Crossing

• Pass a pole/object: time = length of train / relative speed.
• Two trains crossing/overtaking: time = (length₁ + length₂) / relative speed.
• Crossing a platform: time = (length of train + length of platform) / speed of train.
• Length unit note: express lengths in metres when speed in m/s for direct division.

Boats and Streams

• Upstream speed: u_up = u (boat in still water) - v (stream).
• Downstream speed: u_down = u + v.
• Time calculation: use T = distance / upstream or downstream speed as appropriate.

Distance-Time and Speed-Time Graphs

• Distance-time graph: slope = speed; straight line ⇒ uniform speed; steeper ⇒ higher speed.
• Speed-time graph: area under curve = distance covered (use rectangles/triangles for piecewise constant speeds).
• Interpretation: meeting/overtaking can be read from intersection points on distance-time graphs.

Exam Tips and Shortcuts

• Always check units first; convert km/h↔m/s to match metres/seconds or kilometres/hours.
• Use relative speed for all meeting/overtaking questions; set up equations using D = S×T.
• For round trips compute total time separately for each leg when speeds differ; then use total distance/total time for average.
• Common mistakes: averaging speeds directly without weighting by time or distance.