Physics — Motion and Force

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision.

Key Equations of Motion (Linear Motion)

For an object with uniform acceleration:

• v = u + at (velocity–time relation)
• s = ut + ½at² (displacement–time relation)
• v² = u² + 2as (velocity–displacement relation)

Where: u = initial velocity (m/s), v = final velocity (m/s), a = acceleration (m/s²), s = displacement (m), t = time (s).

Example: A car accelerates from rest (u = 0) at 2 m/s² for 5 s. Final velocity v = 0 + (2)(5) = 10 m/s. Distance covered s = (0)(5) + ½(2)(5)² = 25 m.

Newton’s Three Laws

1. First Law (Law of Inertia): A body at rest stays at rest, and a body in motion stays in motion with constant velocity, unless acted upon by an external force. This is also called the law of inertia. Inertia = resistance to change in motion. Mass is the quantitative measure of inertia — a 10 kg block is harder to accelerate than a 2 kg block.

2. Second Law: Force equals mass times acceleration. F = ma. 1 Newton is the force that accelerates 1 kg by 1 m/s². This law gives us the quantitative relationship between force, mass, and acceleration.

3. Third Law: For every action, there is an equal and opposite reaction. Forces always occur in pairs. When you push a wall, the wall pushes back on you with equal force in the opposite direction.

Types of Motion

• Linear: Motion along a straight line. Example: a car moving on a straight road.
• Circular: Motion along a circle. Example: a stone whirled in a horizontal circle. Centripetal acceleration a = v²/r directed towards the centre.
• Oscillatory: Motion that repeats back and forth. Example: a pendulum bob swinging 10 cm left, then 10 cm right. Period T = 2π√(l/g) for a simple pendulum of length l.

Friction

Friction opposes motion between surfaces in contact.

• Static friction (fₛ): Maximum force needed to start motion. fₛ(max) = μₛN where μₛ is the coefficient of static friction and N is the normal reaction.
• Kinetic friction (fₖ): Force opposing motion once it has started. fₖ = μₖN.

⚡ Exam Tip: For UPTET Science, memorise the three equations of motion. A common question type: “A bus travelling at 36 km/h is brought to rest in 10 s. Find the retardation.” Convert 36 km/h = 10 m/s. Use v = u + at: 0 = 10 + a(10) → a = −1 m/s² (retardation = 1 m/s²). Always convert km/h to m/s by dividing by 3.6 before substituting into formulas.

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding.

Gravity and Free Fall

All objects near Earth’s surface accelerate downward at g = 9.8 m/s² (often approximated as 10 m/s² for quick calculations). The weight of a body is W = mg. In free fall (no air resistance), all objects fall at the same rate regardless of mass — Galileo demonstrated this from the Leaning Tower of Pisa. In practice, air resistance means a feather falls slower than a stone. Terminal velocity is reached when air resistance equals the weight of the falling object (about 54 m/s for a human in free fall position).

Derivation of s = ut + ½at²

Starting from v = u + at, the velocity–time graph is a straight line with slope = acceleration. The area under the v–t graph equals displacement. The area consists of a rectangle (u × t) plus a triangle (½ × t × at) = ut + ½at². This derivation frequently appears in UPTET.

Applications of Newton’s Laws in Daily Life

• First Law (Inertia): Passengers lurch backward when a bus suddenly starts — their bodies tend to stay at rest. Seat belts prevent this. Objects slide off a rapidly spinning turntable because they tend to maintain their original circular motion.
• Second Law (F = ma): Pushing a shopping cart (mass constant) with twice the force produces twice the acceleration. A loaded cart (greater mass) accelerates less for the same applied force.
• Third Law (Action–Reaction): A rocket expels gas backward (action); the gas pushes the rocket forward (reaction). Walking: foot pushes backward on ground (action); ground pushes foot forward (reaction).

Circular Motion Details

For an object moving in a circle of radius r with speed v:

• Centripetal force required: F = mv²/r (directed towards the centre)
• Centripetal acceleration: a = v²/r

Common misconception: there is no “centrifugal force” acting on the object — it is a pseudo-force felt in a rotating frame. For a stone whirled in a horizontal circle, tension in the string provides the centripetal force.

Simple Pendulum

A simple pendulum executes oscillatory motion. For small angles (θ < 15°), the time period is T = 2π√(l/g). Factors affecting period: length of the string (T ∝ √l — quadrupling length doubles the period), gravitational acceleration (T ∝ 1/√g), mass does not affect T. This is why a grandfather clock keeps time — a longer pendulum has a longer period.

⚡ UPTET Common Mistakes:

1. Forgetting to convert km/h to m/s before using the equations of motion.
2. Confusing acceleration with velocity — acceleration is rate of change of velocity, not speed. A body can have acceleration but zero velocity (at the turning point of vertical motion), and vice versa (constant speed in circular motion has acceleration due to direction change).
3. Taking g as 10 m/s² in formulas involving g and then using 9.8 — stay consistent.
4. Thinking friction always opposes motion — technically, it opposes relative motion or impending motion between surfaces.

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🔴 Extended — Deep Study (3mo+)

Comprehensive theory for students with extended preparation time.

Projectile Motion — A Combination of Linear and Vertical Motion

Projectile motion splits into independent horizontal and vertical components:

• Horizontal: Constant velocity (no acceleration, ignoring air resistance). vₓ = u cosθ, sₓ = vₓ × t.
• Vertical: Uniformly accelerated motion under gravity. vᵧ = u sinθ − gt, sᵧ = u sinθ × t − ½gt².

Time of flight: T = 2u sinθ / g. Maximum height: H = u² sin²θ / 2g. Range: R = u² sin2θ / g. For a projectile launched and landed at the same horizontal level, maximum range occurs at θ = 45°.

At the highest point, vertical velocity = 0 but acceleration = g (downward). This surprises students — velocity is minimum (zero) but acceleration is maximum.

Non-Uniform Acceleration

When acceleration is not constant, the kinematic equations do not apply directly. The relationship a = dv/dt and v = ds/dt must be integrated. For a body starting from rest with acceleration a = kt (where k is constant), v = ½kt² and s = ⅙kt³. These appear in NEET/JEE but not typically in UPTET — know the principle for context.

Momentum and Impulse

Linear momentum p = mv (kg·m/s). Newton’s second law in momentum form: F = Δp/Δt. Impulse J = FΔt = Δp. This is particularly useful in collision problems. For a rubber ball bouncing off a wall: if it rebounds with the same speed, the change in momentum is 2mv — twice the momentum transfer compared to sticking to the wall (which gives Δp = mv).

Work, Energy, and Power

• Work done: W = Fs cosθ (in joules, J). Only the component of force parallel to displacement does work.
• Kinetic energy: KE = ½mv². A 1 kg object moving at 10 m/s has KE = ½(1)(100) = 50 J.
• Potential energy (gravitational): PE = mgh. A 2 kg book on a 3 m shelf has PE = 2 × 9.8 × 3 = 58.8 J.
• Work–Energy Theorem: Net work done = change in kinetic energy.
• Conservation of Mechanical Energy: In the absence of non-conservative forces (friction, air resistance), KE + PE = constant.
• Power: Rate of doing work. P = W/t = Fv (in watts). A 60 W bulb consumes 60 J per second.

⚡ Previous Year UPTET/NEET Focus: Projectile motion questions frequently appear in combined science papers. Know that at maximum height, the velocity is entirely horizontal (vᵧ = 0). For a body thrown vertically upward, velocity at the point of projection equals velocity at the point of return (sign reversed) — the time to go up equals the time to come down (symmetry). Friction coefficient μ has no unit — it is dimensionless.

⚡ NEET/JEE Exam Tips: For numerical problems in NEET/JEE from this topic, always check whether the question specifies “assuming no air resistance.” In free-fall problems with two masses (e.g., a feather and a stone in vacuum), they hit the ground simultaneously. For pulley problems, tension is the same on both sides of a light, frictionless pulley. The acceleration of the system a = (m₂ − m₁)g / (m₁ + m₂) for two masses connected by a string over a frictionless pulley.

⚡ Common Errors to Flag:

1. Using the wrong sign for acceleration (downward acceleration in upward motion = −g).
2. Mixing up the formulas — write out the three equations of motion and mark knowns/unknowns before selecting which equation to use.
3. In circular motion, students sometimes forget the centripetal force direction is always towards the centre, not along the tangent.