Motion, force, work and energy

Why it matters

A patrol jeep speeding up, a constable pushing a stalled vehicle, a stone falling from a building — all are examples of motion, force, work and energy, the base of Physics.

Plain definitions:

• Motion — change in a body's position with time.
• Force — a push or a pull that can change a body's state of rest or motion, its direction, or its shape.
• Work — done when a force moves a body through some displacement.
• Energy — the capacity (ability) to do work.

Where it appears in the Constable paper: Questions from this area are usually short — a unit, a law, a vector/scalar choice, an everyday example of inertia, or a one-step calculation. Quick marks if your basics and units are clear.

Core concept

Level 1 — Beginner: describing motion

Distance vs displacement

• Distance = total length of the path travelled — a scalar (only size).
• Displacement = shortest straight-line distance from start point to end point, with direction — a vector.

If Suresh walks 3 km east and then 3 km back west, distance = 6 km but displacement = 0. Size of displacement is always less than or equal to distance.

Speed, velocity and acceleration

Quantity	Formula	SI unit	Type
Speed	distance ÷ time	m/s	Scalar
Velocity	displacement ÷ time	m/s	Vector
Acceleration	change in velocity ÷ time	m/s²	Vector

• Uniform motion — equal distances in equal intervals of time (constant speed in a straight line).
• Retardation (deceleration) — negative acceleration; the body slows down.
• Unit change: km/h → m/s, multiply by 5/18; m/s → km/h, multiply by 18/5. So 72 km/h = 72 × 5/18 = 20 m/s.

Why a body moving in a circle at constant speed is accelerating: its direction changes every moment, so its velocity changes — and any change in velocity (size or direction) is acceleration. So uniform circular motion is accelerated motion.

Scalars and vectors (very common question):

Scalars (size only)	Vectors (size + direction)
Distance, speed, mass, time, work, energy, power	Displacement, velocity, acceleration, force, momentum, impulse, weight

Level 2 — Intermediate: equations of motion and graphs

For straight-line motion with constant acceleration (u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement):

1. v = u + at
2. s = ut + ½at²
3. v² = u² + 2as

"Starts from rest" means u = 0. "Comes to rest" means v = 0.

Free fall: Near the Earth's surface, every freely falling body has the same acceleration, g ≈ 9.8 m/s² (questions often say "take g = 10 m/s²"). In a vacuum a feather and a coin fall together; in air the feather is slowed by air resistance, not by its small mass. For a body thrown up, use a = −g; at the highest point its velocity is zero (but its acceleration is still g, downward).

Graphs:

• Slope of a distance–time graph = speed.
• Slope of a velocity–time graph = acceleration.
• Area under a velocity–time graph = displacement.

Level 3 — Newton's laws, momentum and friction

First law (law of inertia): A body stays at rest, or keeps moving in a straight line at constant speed, unless an external force acts on it. Inertia is a body's tendency to resist change in its state. Mass is the measure of inertia — a loaded lorry is harder to start or stop than a bicycle.

Second law: Force = rate of change of momentum; for constant mass this gives F = ma. SI unit: newton (N), where 1 N = 1 kg × 1 m/s². (CGS unit: dyne; 1 N = 10⁵ dyne.)

Third law: For every action there is an equal and opposite reaction. Action and reaction act on two different bodies, so they never cancel each other. Examples: walking (foot pushes ground back, ground pushes foot forward), swimming, a rocket (gases pushed down/back, rocket pushed up/forward), recoil of a gun.

Momentum: p = mv (vector, SI unit kg m/s). Law of conservation of momentum: if no external force acts, the total momentum of a system stays constant. When a gun fires, bullet goes forward and gun recoils backward with equal and opposite momentum.

Impulse = force × time = change in momentum (unit N s). For the same change in momentum, a longer time means a smaller force — why a fielder pulls his hands back while catching, and why vehicles have airbags.

Mass vs weight: Mass (kg) is the amount of matter and is the same everywhere. Weight is the force of gravity on the body, W = mg, in newton. On the Moon, g is about one-sixth of Earth's, so weight becomes about one-sixth but mass stays the same.

Friction opposes relative motion between surfaces in contact. Rolling friction is smaller than sliding friction — hence wheels and ball bearings.

Level 4 — Advanced: work, energy and power

Work: W = F × s × cos θ, where θ is the angle between force and displacement. Work is a scalar; SI unit joule (J) (1 J = 1 N × 1 m; CGS unit erg, 1 J = 10⁷ erg).

Case	Angle θ	Work	Example
Force along motion	0°	Positive (maximum)	Pulling a cart forward
Force perpendicular to motion	90°	Zero	Satellite in circular orbit; coolie walking on level road (work against gravity)
Force opposite to motion	180°	Negative	Friction on a sliding box; brakes
No displacement	—	Zero	Pushing a wall; holding a suitcase still

Kinetic energy (energy of motion): KE = ½mv². Because of v², doubling speed makes KE 4 times; tripling makes it 9 times.

Potential energy (energy of position or shape): PE = mgh at height h. A stretched bow or compressed spring stores elastic PE.

KE and momentum link: KE = p²/2m. For the same momentum, the lighter body has more KE. For the same KE, the heavier body has more momentum.

Law of conservation of energy: Energy can neither be created nor destroyed; it only changes form, and the total stays constant. For a falling stone (ignoring air), PE lost = KE gained. In a swinging pendulum, KE is maximum at the middle (mean) position and PE is maximum at the extreme positions.

Common energy conversions:

Device	Conversion
Electric cell / battery	Chemical → Electrical
Electric motor (fan)	Electrical → Mechanical
Generator / dynamo	Mechanical → Electrical
Solar cell	Light → Electrical
Loudspeaker	Electrical → Sound

Power = rate of doing work = work ÷ time. SI unit watt (W) = 1 J/s. 1 horsepower (hp) ≈ 746 W. The commercial unit of electrical energy is the kilowatt-hour (kWh), the "unit" on your electricity bill: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J. Note: kWh is a unit of energy, not power.

Worked examples

Example 1 — Equations of motion. A car starts from rest and reaches 20 m/s in 5 s. Find its acceleration and the distance covered.

• u = 0, v = 20 m/s, t = 5 s.
• a = (v − u)/t = 20/5 = 4 m/s².
• s = ut + ½at² = 0 + ½ × 4 × 25 = 50 m.

Example 2 — Average speed trap. A constable rides to a village at 40 km/h and returns on the same road at 60 km/h. Average speed?

• Wrong: (40 + 60)/2 = 50 km/h.
• Right: for equal distances, average speed = 2xy/(x + y) = (2 × 40 × 60)/100 = 48 km/h.
• Check: one way 120 km → 3 h + 2 h = 5 h for 240 km = 48 km/h. The slower trip takes more time, pulling the average below 50.

Example 3 — Free fall. A stone is dropped from a height of 45 m (g = 10 m/s²). Find the time to reach the ground and its speed on hitting the ground.

• s = ½gt² → 45 = 5t² → t² = 9 → t = 3 s.
• v = gt = 10 × 3 = 30 m/s. (Check: v² = 2gh = 2 × 10 × 45 = 900, v = 30.)

Example 4 — Recoil of a gun. A 4 kg gun fires a 20 g bullet at 400 m/s. Find the recoil speed of the gun.

• Total momentum before firing = 0, so gun's momentum = bullet's momentum (conservation of momentum).
• 4 × V = 0.02 × 400 = 8 → V = 2 m/s backward. (Convert 20 g to 0.02 kg first.)

Example 5 — Work, PE and power. A 60 kg constable climbs stairs 10 m high in 12 s (g = 10 m/s²). Work done against gravity and power?

• Work = mgh = 60 × 10 × 10 = 6000 J.
• Power = 6000/12 = 500 W.
• Only vertical height counts against gravity.

Real-world connection

• Seat belts: When a bus brakes suddenly, your body keeps moving forward (inertia of motion); belts and airbags stop you safely. When a bus starts suddenly, standing passengers fall backward (inertia of rest).
• Braking distance: KE = ½mv², so at double speed a vehicle has four times the energy and, with the same braking force, needs about four times the distance to stop — why speed limits matter.
• Sand pits in long jump increase stopping time, reducing the force on the body.

How it is asked in the exam

With about 54 seconds per question and no calculator, formats are short:

1. Direct fact / unit: "SI unit of power?" → watt. "1 kWh = ___ J" → 3.6 × 10⁶.
2. Vector-scalar: "Which is a vector?" (speed, work, momentum, energy) → momentum.
3. Law behind an example: "A rocket works on ___" → Newton's third law (conservation of momentum). "Passengers fall forward when a bus stops suddenly" → inertia of motion.
4. Match the following: devices–energy conversions, quantities–units.
5. One-step numerical: acceleration, force, KE, PE, power, free fall, recoil — with easy numbers.

Difficulty levels:

• Easy (15–25 s): units, definitions, scalar/vector, laws.
• Medium (30–50 s): one formula — v = u + at, KE = ½mv², power = W/t, km/h to m/s.
• Hard (about 60 s; do these last): percentage change of KE, same-momentum comparisons, average speed, two-step free fall.

No negative marking — never leave a question blank; eliminate by units and choose.

తెలుగు సారాంశం (Telugu summary)

చలనం అంటే కాలంతో పాటు వస్తువు స్థానం మారడం. దూరం అదిశ రాశి (మొత్తం ప్రయాణించిన మార్గం); స్థానభ్రంశం సదిశ రాశి (మొదటి, చివరి స్థానాల మధ్య అతి తక్కువ దూరం, దిశతో సహా).
వడి = దూరం ÷ కాలం; వేగం = స్థానభ్రంశం ÷ కాలం; త్వరణం = వేగంలో మార్పు ÷ కాలం, దీని ప్రమాణం m/s².
చలన సమీకరణాలు: v = u + at, s = ut + ½at², v² = u² + 2as. km/h ను m/s గా మార్చడానికి 5/18 తో గుణించాలి.
న్యూటన్ మొదటి నియమాన్ని జడత్వ నియమం అంటారు; ద్రవ్యరాశి జడత్వానికి కొలత. రెండో నియమం F = ma, బలానికి ప్రమాణం న్యూటన్.
మూడో నియమం: ప్రతి చర్యకు సమానమైన, వ్యతిరేకమైన ప్రతిచర్య ఉంటుంది; ఇవి రెండు వేర్వేరు వస్తువులపై పనిచేస్తాయి కాబట్టి ఒకదానినొకటి రద్దు చేయవు.
ద్రవ్యవేగం p = mv. బాహ్య బలం లేకపోతే మొత్తం ద్రవ్యవేగం స్థిరంగా ఉంటుంది — తుపాకీ వెనక్కి తన్నడం, రాకెట్ ఇందుకు ఉదాహరణలు.
బరువు W = mg (న్యూటన్లలో); చంద్రుడిపై బరువు సుమారు ఆరో వంతు అవుతుంది, కానీ ద్రవ్యరాశి మారదు.
పని W = F × s × cosθ; బలం స్థానభ్రంశానికి లంబంగా ఉన్నా, స్థానభ్రంశం సున్నా అయినా పని సున్నా. పని, శక్తి రెండింటి ప్రమాణం జౌల్.
గతిజ శక్తి = ½mv² (వేగం రెట్టింపైతే గతిజ శక్తి నాలుగు రెట్లు); స్థితిజ శక్తి = mgh. శక్తిని సృష్టించలేము, నాశనం చేయలేము; ఒక రూపం నుంచి మరో రూపానికి మాత్రమే మారుతుంది.
సామర్థ్యం = పని ÷ కాలం, ప్రమాణం వాట్; 1 hp ≈ 746 W; 1 kWh = 3.6 × 10⁶ J — ఇది శక్తికి ప్రమాణం, సామర్థ్యానికి కాదు.

Key terms (English — తెలుగు):

• Distance — దూరం
• Displacement — స్థానభ్రంశం
• Speed — వడి
• Velocity — వేగం
• Acceleration — త్వరణం
• Force — బలం
• Inertia — జడత్వం
• Mass — ద్రవ్యరాశి
• Weight — బరువు
• Momentum — ద్రవ్యవేగం
• Impulse — ప్రచోదనం
• Work — పని
• Energy — శక్తి
• Kinetic energy — గతిజ శక్తి
• Potential energy — స్థితిజ శక్తి
• Power — సామర్థ్యం
• Scalar — అదిశ రాశి
• Vector — సదిశ రాశి