JEE/NEET Physics · Motion in a Straight Line series · Part 6 of 6 · All parts →
- The whole series on one card — memorise the card, not the chapters
- distance vs displacement · avg speed = total d ÷ total t · v² = u² + 2as
- x-t slope = v · v-t slope = a, area = s · a-t area = Δv
- Free fall: same g for all · H = u²/2g · T = 2u/g
- Relative: subtract the observer · same −, opposite +
The final card of the Motion in a Straight Line series — six parts compressed into one revision sheet, plus the story of how these four equations landed humans on the Moon.
- The master formula card
- The one-rule-per-part recap
- Kinematics in the real world
- Final practice set
- Recap
The Master Formula Card
| What | Formula / rule | Remember |
|---|---|---|
| Distance vs displacement | path vs straight arrow | closed loop → Δx = 0 |
| Average speed | total distance ÷ total time | never average speeds |
| Average velocity | Δx ÷ Δt | signed |
| Acceleration | a = (v − u)/t | m/s², vector |
| Golden equation 1 | v = u + at | no s |
| Golden equation 2 | s = ut + ½at² | no v |
| Golden equation 3 | v² = u² + 2as | no t |
| x-t graph | slope = velocity | flat = rest |
| v-t graph | slope = a · area = s | signed area! |
| a-t graph | area = Δv | slope of nothing above it |
| Free fall | a = g = 9.8 for ALL masses | top: v = 0, a = g |
| Vertical throw | H = u²/2g · T = 2u/g | symmetric trip |
| Relative velocity | v_A − v_B | same −, opposite + |
| River crossing | t_min = d/b | straight needs b > s |
The One-Rule-Per-Part Recap
Part 1: distance is the meter, displacement is the arrow. Part 2: acceleration is changing velocity — the three golden equations solve any constant-a story. Part 3: slope goes down the graph stack, area goes up. Part 4: gravity accelerates everything equally — signs are everything. Part 5: velocity belongs to a pair — subtract the observer.
Kinematics in the Real World
- Apollo 11’s landing computer ran these exact equations — the lunar descent was v² = u² + 2as with a live rocket throttle: 1.6 m/s² of Moon gravity, solved 30 times a second.
- Airbags extend your stopping time from 1 ms to 100 ms — in a = Δv/Δt, tenfold more time means tenfold less acceleration on your body: the equation between a crash and a bruise.
- Runway design is v² = u² + 2as solved backwards — required runway length scales with the SQUARE of takeoff speed: why long-haul planes need 3 km and small props need 1 km.
- Sports slow-motion ‘speed at impact’ graphics — free-fall results: a ball dropped from 2 m arrives at √(2×9.8×2) ≈ 6.3 m/s, every time, every ball.
- Galileo’s inclined-plane experiments started it all — by diluting gravity down a groove he made time measurable at all: this chapter is the 400-year-old seed of all modern physics.
Before Newton could write laws of forces, someone had to describe motion itself precisely — what velocity means, what acceleration means, how they connect. Galileo built that dictionary; Newton then answered the next question (‘what CAUSES acceleration?’). Kinematics is the grammar of the language every later chapter speaks.
Moon landing descent: from 1600 m/s at 15 km altitude to a soft 0 m/s touchdown — engineers solved v² = u² + 2as with a = (thrust − 1.6)/m, live, with fuel and mass changing: the same three-line toolkit from Part 2, iterated by a computer the size of a suitcase.
Picture the three graph panels (x-t, v-t, a-t) as one building: slope takes you down a floor, area takes you up. Every mechanics problem ever set is a journey through these floors — start where the data lives, move one floor at a time, exit where the question lives.
Practice set (answers hidden — try first)
(NEET-level) 90 km/h ÷ 3.6 = ? m/s:
(JEE Main-level) v = 0, u = 20, a = −4: distance =
(NEET-level) v-t rectangle 10 m/s × 12 s: displacement =
(JEE Main-level) Two objects dropped together from different heights hit with speeds 10 and 20 m/s. Height ratio =
(NEET-level) You (5 m/s) pass a jogger (3 m/s, same way). Relative speed =
- distance vs displacement; avg speed = d_total/t_total
- v = u + at · s = ut + ½at² · v² = u² + 2as
- graphs: slope down, area up
- free fall: g for all; H = u²/2g, T = 2u/g
- relative velocity: subtract the observer
- 🔁 the 15-row master card
- 🔁 one rule per part
- 🔁 kinematics = grammar of physics
- 🧠 Full-card chant: ‘arrow it, accelerate it, graph it, drop it, subtract the seer’.
- 🏠 Daily: airbags buy time = divide acceleration.
- 🏠 Daily: the Moon landing ran Part 2’s equations live.
Quick revision
- The whole series on one card — memorise the card, not the chapters
- distance vs displacement · avg speed = total d ÷ total t · v² = u² + 2as
- x-t slope = v · v-t slope = a, area = s · a-t area = Δv
- Free fall: same g for all · H = u²/2g · T = 2u/g
- Relative: subtract the observer · same −, opposite +
- The one-rule-per-part recap
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