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Physics · AFCAT

PA02 — Mechanics: Motion, Force, Work & Power

✈ Physics – PA02  ·  AFCAT General Awareness AFCAT Level ★ High Priority

Mechanics is the backbone of AFCAT Physics. Newton’s three laws, the equations of motion, and work-energy concepts together contribute the highest number of Physics questions in AFCAT. The questions are Class 10 level — concept-based and application-oriented, not calculus. Master this chapter and you score 1–2 guaranteed questions.

📌 AFCAT Focus: Questions here test Newton’s laws with real-life examples (recoil of a gun, rocket propulsion, why a person jerks forward when a bus brakes), the work-energy theorem, and simple F = ma calculations. Equations of motion are used to find final velocity or distance — especially free-fall problems (g = 10 m/s²).
PART 1 — KINEMATICS

1. Equations of Motion (Uniform Acceleration)

When an object accelerates uniformly (constant acceleration), three equations connect initial velocity, final velocity, acceleration, time, and displacement. These are used in every AFCAT mechanics numerical.

Fig. 1 — Three Equations of Motion — When to Use Each
THREE EQUATIONS OF MOTION — Uniform Acceleration v = u + at Use when: displacement is NOT needed. You know u, a, t and want v. u = initial velocity (m/s) v = final velocity (m/s) a = acceleration (m/s²), t = time (s) s = ut + ½at² Use when: final velocity is NOT needed. Find distance covered in time t. s = displacement (m) Free fall: u=0, a=g ≈ 10 m/s² s = ½gt² when starting from rest v² = u² + 2as Use when: time is NOT given or needed. Velocity from distance & acceleration. Most used in AFCAT! Free fall: v² = 2gh (u=0) v = √(2gh) at ground For FREE FALL: u = 0, a = g = 10 m/s² downward  |  For object thrown UP: a = −g, at peak v = 0
✎ Worked Example — Free Fall
A stone is dropped from a height of 45 m. How long does it take to reach the ground? (g = 10 m/s²)
Dropped means u = 0. Use s = ut + ½at²
45 = 0 + ½ × 10 × t²
45 = 5t² → t² = 9 → t = 3 seconds
✔ Time = 3 s
PART 2 — NEWTON’S LAWS

2. Newton’s Three Laws of Motion

These three laws are the most tested concept in AFCAT Mechanics. Focus on real-life applications — AFCAT asks “which law explains this?” rather than mathematical derivations.

Fig. 2 — Newton’s Three Laws with Real-Life Examples
NEWTON'S THREE LAWS — Statement, Concept & Real Examples FIRST LAW Law of Inertia Statement: A body at rest stays at rest; a body in motion stays in motion — unless a net force acts on it. Key concept: Inertia ∝ mass (heavier = harder to move) Real examples: • Passenger jerks forward when bus stops suddenly • Coin on card falls into glass when card is flicked SECOND LAW F = ma Statement: Net force = mass × acceleration: F = ma Greater F → greater a Greater m → smaller a Impulse: J = F × t = Δp = m(v−u) Momentum p = mv Real examples: • More force on cricket ball → more acceleration • Airbag: spreads force over time → reduces impact force THIRD LAW Action & Reaction Statement: Every action has an equal & opposite reaction — on DIFFERENT bodies. They never cancel each other. Key point: Action on body A Reaction on body B Real examples: • Gun recoils when bullet fires (GUN ← BULLET →) • Rocket: exhaust back, rocket goes forward
⚠ AFCAT Trap — Gun Recoil: When a gun fires a bullet, which law explains the recoil? Third Law. The bullet goes forward (action) → gun recoils backward (reaction). Conservation of momentum also applies: total initial momentum = 0; total final momentum = 0. So gun momentum = −bullet momentum.
PART 3 — WORK, ENERGY & POWER

3. Work, Energy & Power

Core Formulae — Know These Cold:

● Work  W = F × s × cosθ    [Unit: Joule (J)]
    Work = 0 when force ⊥ displacement (θ = 90°) — e.g., carrying load horizontally

● Kinetic Energy  KE = ½mv²    [Unit: Joule]
● Potential Energy  PE = mgh    [Unit: Joule]
● Conservation of Energy: KE + PE = constant (no friction)

● Power  P = W/t = F×v    [Unit: Watt (W) = J/s]
    1 horse power (HP) = 746 W ≈ 750 W

▶ When is Work ZERO?

  • Force perpendicular to displacement (θ = 90°)
  • Carrying a bag horizontally — gravity is vertical, motion is horizontal
  • A satellite in circular orbit — gravity ⊥ velocity
  • Uniform circular motion — centripetal force ⊥ speed

▶ KE & Momentum Relationship

  • Momentum: p = mv
  • KE = p²/(2m)
  • KE doubles → momentum ×√2
  • KE × 4 → momentum × 2
  • Elastic collision: both KE & momentum conserved
  • Inelastic: only momentum conserved
✎ Worked Example — Work Done
A person pushes a box with 50 N force over 4 m on a horizontal floor. Find work done. Then find power if it takes 8 seconds.
Work = F × s = 50 × 4 = 200 J (θ = 0°, cos0° = 1)
Power = W/t = 200/8 = 25 W
✔ W = 200 J  |  P = 25 W

4. Friction

Fig. 3 — Types of Friction and Their Properties
FRICTION TYPES — Largest to Smallest: Static > Kinetic > Rolling STATIC Highest of the three Acts before motion begins. Adjusts from 0 up to its maximum (limiting friction) f = μsN Example: Box at rest on floor — hard to start pushing it. μs = coefficient of static friction (largest) KINETIC Less than static friction Acts during sliding motion. Less than static friction μk < μs (always) f = μkN Example: Book sliding across a table. Easier to keep moving than to start moving. μk < μs (medium) ROLLING Smallest of the three Acts when object rolls. Contact is essentially a point → least resistance μr < μk < μs Example: Ball rolling on floor. Car tyres on road. Ball bearings replace sliding with rolling!
💡 Friction is Independent of Surface Area: The friction force does NOT depend on how much surface area is in contact — only on the normal force (N) and the coefficient (μ). This is a direct AFCAT question. Ball bearings reduce friction by converting sliding friction to rolling friction.

5. Circular Motion & Centripetal Force

Circular Motion Formulae:

● Centripetal Force: F = mv²/r   (directed toward the centre)
● Centripetal Acceleration: a = v²/r
● Angular velocity: ω = 2π/T = 2πf
● Work done by centripetal force = 0 (force ⊥ velocity always)

What provides centripetal force?
• Ball on string → tension in string
• Planet around Sun → gravity
• Car on curve → friction between tyres and road
• Electron around nucleus → electrostatic force

📝 AFCAT PYQs — Mechanics

Q1. A rocket works on the principle of: AFCAT PYQ
(a) Newton’s First Law (b) Newton’s Second Law (c) Newton’s Third Law (d) Law of Gravitation
✔ Answer: (c) Newton’s Third Law
In a rocket, hot gases are expelled backward at high speed (action). The rocket moves forward with equal and opposite reaction force. This is Newton’s Third Law in action. Rockets work in vacuum too — they don’t need air to push against.
Q2. A body is moving with uniform velocity. The net force acting on it is: AFCAT PYQ
(a) Increasing (b) Decreasing (c) Zero (d) Equal to its weight
✔ Answer: (c) Zero
Newton’s First Law: a body in uniform motion stays so unless acted on by a net external force. Uniform velocity means zero acceleration. From F = ma, if a = 0, then F = 0. This is a direct, repeatedly tested question in AFCAT.
Q3. The kinetic energy of an object is doubled. By what factor does its momentum change? ⚡ Tricky
(a) 2 times (b) 4 times (c) √2 times (d) 1/2 times
✔ Answer: (c) √2 times
KE = p²/(2m) → p = √(2m·KE). If KE doubles: new p = √(2m × 2KE) = √2 × √(2m·KE) = √2 × old p. Rule: KE × 4 → momentum × 2; KE × 2 → momentum × √2.
Q4. A person is carrying a suitcase horizontally. The work done against gravity is: AFCAT PYQ
(a) Positive (b) Negative (c) Zero (d) Equal to mgh
✔ Answer: (c) Zero
Work = F × s × cosθ. Gravity acts downward; displacement is horizontal. The angle between them is 90°. cos 90° = 0 → Work = 0. No work is done against gravity when moving horizontally. Height doesn’t change, so PE doesn’t change either.
Q5. Which of the following friction types is the smallest in magnitude? AFCAT PYQ
(a) Static friction (b) Kinetic friction (c) Rolling friction (d) All are equal
✔ Answer: (c) Rolling friction
Order: Static > Kinetic > Rolling. Rolling friction is smallest because the contact area at any instant is essentially a point (or line), and no sliding occurs. This is why wheels and ball bearings are used — to convert sliding friction into much smaller rolling friction.

🧠 Quick Memory Chart — PA02 Mechanics

📎 3 Equations of Motion
  • v = u + at (no s)
  • s = ut + ½at² (no v)
  • v² = u² + 2as (no t)
  • Free fall: u=0, a=g=10
  • v = √(2gh) at ground
⚡ Newton’s Laws
  • 1st: Inertia (no force → no change)
  • 2nd: F = ma (more F → more a)
  • 3rd: Rocket, gun recoil, swimming
  • Inertia ∝ mass (not weight)
  • Uniform v → F = 0
▶ Work, Energy & Friction
  • W = 0 when F ⊥ s (90°)
  • KE = ½mv²; PE = mgh
  • Friction: static > kinetic > rolling
  • KE doubles → momentum ×√2
  • Power = W/t = Fv

📝 Practice Exercise — Attempt Before Checking

E1. A ball is dropped from 80 m height. Its speed just before hitting ground is (g = 10 m/s²):
(a) 40 m/s (b) 80 m/s (c) 20 m/s (d) 10 m/s
E2. A gun fires a bullet. Which physical quantity is conserved?
(a) Kinetic energy (b) Momentum (c) Potential energy (d) Velocity
E3. A 60 W bulb is used for 5 hours. Energy consumed in kWh is:
(a) 0.6 kWh (b) 0.3 kWh (c) 6 kWh (d) 300 kWh
E4. Newton’s second law connects force with:
(a) Velocity (b) Momentum change rate (c) Distance (d) Inertia
E5. The centripetal force on a body moving in a circle does:
(a) Positive work (b) Negative work (c) Zero work (d) Maximum work at top
Answers:
E1 → (c) 20 m/s  [v = √(2gh) = √(2×10×80) = √1600 = 40 m/s... wait: √(2×10×80) = √1600 = 40 m/s → Answer is (a) 40 m/s]  |  E2 → (b) Momentum  [Conservation of momentum always holds; KE may not be conserved in inelastic collisions]  |  E3 → (b) 0.3 kWh  [E = 0.06 kW × 5 h = 0.3 kWh]  |  E4 → (b) Rate of change of momentum  [F = dp/dt = ma]  |  E5 → (c) Zero work  [Centripetal force always ⊥ velocity; W = Fs cos90° = 0]
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