Concept 1
Connect distance, speed and time
Distance = speed × time. Therefore speed = distance ÷ time and time = distance ÷ speed. The relation works only after every quantity uses compatible units.
Proportion: at fixed speed, distance is directly proportional to time; for a fixed distance, speed and time are inversely proportional.
Concept 2
Convert units before calculating
Multiply km/h by 5/18 to obtain m/s; multiply m/s by 18/5 to obtain km/h. Convert minutes to hours or seconds when the distance unit requires it.
| Quantity | Conversion | Example |
|---|---|---|
| km/h to m/s | × 5/18 | 72 km/h = 20 m/s |
| m/s to km/h | × 18/5 | 15 m/s = 54 km/h |
| minutes to hours | ÷ 60 | 45 min = 3/4 h |
Concept 3
Average speed uses total distance and total time
Average speed = total distance ÷ total time. Do not average two speeds unless the time spent at each speed is equal.
For equal distances at speeds a and b, average speed = 2ab/(a+b). For equal times, average speed = (a+b)/2.
Concept 4
Relative speed captures closing or separating motion
For opposite directions, add speeds. For the same direction, subtract the smaller speed from the larger. Meeting or overtaking time = initial separation ÷ relative speed.
Two travellers 210 km apart moving toward each other at 50 and 55 km/h meet in 210/(50+55)=2 hours.
Concept 5
A train must clear the full object length
Passing a pole or person: distance equals train length. Passing a platform: distance equals train length + platform length. Passing another train: use the sum of their lengths with the appropriate relative speed.
A 180 m train at 54 km/h moves at 15 m/s, so it passes a pole in 180/15=12 seconds.
Concept 6
Separate still-water speed from stream speed
Downstream speed = boat speed in still water + stream speed. Upstream speed = boat speed in still water − stream speed.
If downstream speed is d and upstream speed is u, still-water speed = (d+u)/2 and stream speed = (d−u)/2.
Concept 7
Translate race leads and circular laps into distances
If A beats B by 100 m in a 500 m race, then when A covers 500 m, B covers 400 m; their speed ratio is 5:4. Convert a time lead into the distance covered in that time.
On a circular track of length L, runners in opposite directions meet every L/(a+b); in the same direction, the faster laps the slower every L/(a−b).
Worked methods
Examples with reasoning
Basic journey
At 48 km/h for 2.5 hours, distance = 48×2.5 = 120 km.
Equal-distance average
Equal distances at 40 and 60 km/h give average = 2×40×60/(40+60)=48 km/h.
Overtaking
A car at 72 km/h is 150 m behind one at 54 km/h. Relative speed=18 km/h=5 m/s, so catch-up time=30 seconds.
Train and platform
A 150 m train crosses a 250 m platform at 20 m/s. Distance=400 m, so time=20 seconds.
Boat and stream
Downstream speed is 18 km/h and upstream 10 km/h. Still-water speed=14 km/h; stream speed=4 km/h.
Circular track
On a 600 m track, runners at 8 and 4 m/s in the same direction meet every 600/(8−4)=150 seconds.
Exam traps
Errors that break the motion model
Mixed units
Never divide metres by km/h without converting one of them.
Simple speed average
Use total distance ÷ total time unless travel times are equal.
Wrong relative sign
Add for opposite directions; subtract for the same direction.
Ignoring platform length
A train clears a platform only after its full length passes the far edge.
Negative upstream speed
The boat must be faster than the stream to travel upstream.
Confusing a lead
A 100 m lead in a 500 m race means the slower runner covers 400 m.
Original practice
Check understanding after learning
Original syllabus-aligned questions—not claimed previous-year questions.
Rapid revision
The one-minute sheet
- Distance = speed × time; make units compatible first.
- km/h to m/s: ×5/18; m/s to km/h: ×18/5.
- Average speed = total distance ÷ total time.
- Relative speed: add in opposite directions, subtract in the same direction.
- Train clearance distance includes every length that must pass.
- Downstream=b+s; upstream=b−s.
- Circular-track meeting time = track length ÷ relative speed.
Source ledger
Official foundations
- SSC CGL official syllabus: Time and Distance under Mathematical Abilities
- NCERT official chapter: Describing Motion Around Us
- NCERT official textbook portal
Explanations, worked examples and practice are original. Official references are credited and not reproduced. Drafted 25 September 2026.
Algebra and linear graphs.