JEE/NEET Physics · Motion in a Straight Line series · Part 2 of 6 · All parts →
- Acceleration = how quickly velocity CHANGES: a = (v − u)/t, in m/s²
- It’s a vector too: +a speeds you up in the + direction, −a slows you (or speeds you up backwards)
- The three equations (constant a only!): v = u + at · s = ut + ½at² · v² = u² + 2as
- Sign discipline: decide + once, then u, v, a, s all carry signs
- Any two of the five quantities (u, v, a, s, t) given → the third comes from one equation
Velocity tells you how fast; acceleration tells you how fast ‘how fast’ is changing. A car pulling away, a bike braking, a coin dropped from a roof — all three run on the same three equations. Part 2 of the Motion in a Straight Line series.
- What acceleration really is
- Reading the sign of a
- The three golden equations
- Choosing the right one
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
What Acceleration Really Is
Zero acceleration doesn’t mean standing still — it means velocity is unchanging: 80 km/h on a straight highway forever is a = 0. Acceleration begins the moment velocity changes: speeding up, slowing down, or (in later chapters) turning. Its unit, m/s², literally reads ‘metres per second, per second’.
Reading the Sign of a
| Situation | Velocity sign | Acceleration sign | What happens |
|---|---|---|---|
| Moving right, speeding up | + | + | faster right |
| Moving right, braking | + | − | slows, may reverse |
| Moving left, speeding up | − | − | faster left |
| Moving left, braking | − | + | slows |
Same sign = speeding up; opposite signs = braking. ‘Negative acceleration’ does not automatically mean slowing — it means accelerating in the − direction.
The Three Golden Equations
For constant acceleration only, three equations connect the five quantities u (start velocity), v (final velocity), a, s (displacement), t:
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| u | starting velocity (‘u’ for initial) | m/s, signed |
| v | velocity after time t | m/s, signed |
| a | acceleration (constant!) | m/s², signed |
| s | displacement in time t | m, signed |
| t | elapsed time | s |
Choosing the Right One
Inventory what’s given and what’s wanted. No t anywhere? Use v² = u² + 2as. No v? Use s = ut + ½at². No s? Use v = u + at. The right equation is the one that doesn’t contain the quantity nobody mentioned.
Solved Examples
v = 0, u = 20, a = −5: 0 = 20 − 5t → t = 4 s.
✔
Answer: 4 s
No t given → v² = u² + 2as: 0 = 400 + 2(−5)s.
s = 40 m.
Doubling the speed would quadruple this — the u² inside is why highway speeds kill. ✔
Answer: 40 m
Stage 1: s = ½(2)(100) = 100 m, v = 20 m/s.
Stage 2: 0 = 400 − 2(4)s → s = 50 m.
Total = 150 m — always split multi-stage problems at the velocity handover. ✔
Answer: 150 m
- Using the equations when a isn’t constant. They hold ONLY for uniform acceleration — check before plugging.
- Mixing units. km/h must become m/s (÷3.6) before entering any equation with metres.
- Sign chaos. Braking car moving +: u = +20, a = −5 — both signs must appear, or the answer silently flips.
- Stopping-distance intuition. Twice the speed = FOUR times the stopping distance (u² law) — never ‘twice’.
This Physics in Your Daily Life
- ‘0 to 100 in 3 seconds’ car ads are acceleration marketing: 100 km/h in 3 s ≈ 9.3 m/s² — about the same as free fall, which is why fast launches feel like a dropping lift.
- Yellow-light dilemma at crossings — ‘can I stop?’ is v² = u² + 2as solved live by every driver: braking distance grows as speed SQUARED.
- Plane takeoff — a runway is sized for ~2–3 m/s² over 30–40 s: the same s = ut + ½at² with lives at stake.
- Lift journeys — the stomach-flutter at launch is your body feeling ~1.5 m/s² of extra acceleration; cruises are a = 0 and feel like nothing.
- Train metro codes — smooth ±1 m/s² limits are chosen so standing passengers don’t stumble: acceleration, not speed, is what topples people.
A rickshaw wallah negotiating fare by speed is missing the point — passengers care about the JERK of the launch and the lurch of the brake. Speed is how the world slides past; acceleration is what your body actually feels pressed into the seat. You never feel speed in a smooth flight; you feel every change of it.
0→100 km/h in 3 s: velocity changes by 27.8 m/s in 3 s → a ≈ 9.3 m/s², one g. At 40 m/s² (fighter jet, crash): velocity changes by a whole highway speed EVERY second. The m/s² unit says it directly: ‘this many m/s of velocity, gained every second’.
Draw velocity against time: acceleration is the SLOPE of that line. Flat = cruising. Upward tilt = speeding up. Downward = braking. A curving slope = changing acceleration (jerk). Every motion story is one graph, and a is its tilt.
Practice set (answers hidden — try first)
(NEET-level) Rest to 30 m/s at 3 m/s²: time =
(JEE Main-level) u = 0, a = 4, t = 5: displacement =
(NEET-level) v² = u² + 2as with v=0, u=15, s=22.5: |a| =
(Concept) A body moves at constant 80 km/h in a straight line. Its acceleration:
(JEE Main-level) Stopping distance at 20 m/s with a = −5 is 40 m. At 40 m/s:
- a = (v − u)/t, m/s² — rate of velocity change
- same signs = speed up, opposite = brake
- v = u + at · s = ut + ½at² · v² = u² + 2as (constant a only)
- pick the equation missing your unknown
- stopping distance ∝ speed squared
- 🔁 a = Δv/Δt, vector, m/s²
- 🔁 three equations, constant a only
- 🔁 equation choice = skip the unknown
- 🧠 Chant: ‘u-vat, suat, v-u-2as’ — the three tools.
- 🧠 Signs: ‘same sign speeds, opposite brakes’.
- 🧠 Doubling speed quadruples braking distance — the u² law.
- 🏠 Daily: ‘0–100 in 3 s’ ads ≈ free-fall launch feel.
- 🏠 Daily: metro’s ±1 m/s² keeps standing riders upright.
Quick revision
- Acceleration = how quickly velocity CHANGES: a = (v − u)/t, in m/s²
- It’s a vector too: +a speeds you up in the + direction, −a slows you (or speeds you up backwards)
- The three equations (constant a only!): v = u + at · s = ut + ½at² · v² = u² + 2as
- Sign discipline: decide + once, then u, v, a, s all carry signs
- Any two of the five quantities (u, v, a, s, t) given → the third comes from one equation
- What acceleration really is
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