a=dvdt=dvds⋅dsdt=vdvdsa equals d v over d t end-fraction equals d v over d s end-fraction center dot d s over d t end-fraction equals v d v over d s end-fraction v⋅dv=a⋅dsv center dot d v equals a center dot d s Integrating both sides within limits (velocity , and displacement
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At the end of the flight, net vertical displacement is zero ( all important derivations of physics class 11 pdf download
: Comprehensive formulas for the path of a projectile (parabolic trajectory), Time of Flight ( ), Maximum Height ( ), and Horizontal Range ( Vector Addition
Resolving forces horizontally (providing centripetal force): Since friction
Can I provide a sample for the banked road or projectile range equations? Share public link a=dvdt=dvds⋅dsdt=vdvdsa equals d v over d t end-fraction
N(cosθ−μsinθ)=mgcap N open paren cosine theta minus mu sine theta close paren equals m g
: Proof of the conservation of energy for flowing fluids.
💡 When practicing, always draw the associated labeled diagram first. Examiners often award 1–1.5 marks just for a correct, neat diagram in a 5-mark derivation. Important Derivations for Class 11 Physics | PDF - Scribd Important Derivations for Class 11 Physics | PDF
This matches the differential equation for Simple Harmonic Motion (
When a spherical body falls through a viscous fluid, it eventually reaches a constant maximum velocity called terminal velocity ( At equilibrium, Net Downward Force = Net Upward Force.
| | Key Derivations (Must-Know for Exams) | | :--- | :--- | | 1. Physical World | This is a conceptual introduction and does not contain major mathematical derivations. | | 2. Units and Measurements | • Parallax Method & Parallax Errors • Propagation of Errors (Addition, Subtraction, Multiplication, Division) • Dimensional Formula of Physical Quantities | | 3. Motion in a Straight Line | • Kinematic Equations of Motion (v = u + at, s = ut + ½at², v² = u² + 2as) via Graphical and Calculus Methods • Relative Velocity in One Dimension | | 4. Motion in a Plane | • Parallelogram Law of Vector Addition • Expression for Centripetal Acceleration (v²/r) • Projectile Motion (Time of Flight, Maximum Height, Horizontal Range, Equation of Path) | | 5. Laws of Motion | • Derivation of First and Third Law from Newton's Second Law • Impulse-Momentum Theorem • Recoil of a Gun (Conservation of Linear Momentum) • Motion of a Car on a Banked Road (Max Optimum Speed) • Bending of a Cyclist | | 6. Work, Energy, and Power | • Work-Energy Theorem for Constant and Variable Forces • Expression for Kinetic Energy (KE = ½mv²) via Calculus Method • Motion in a Vertical Circle (Tension at Lowest, Mid, and Highest Points) • Elastic and Inelastic Collisions in One Dimension | | 7. System of Particles and Rotational Motion | • Torque = r × F • Relation between Torque and Angular Momentum (τ = dL/dt) & Moment of Inertia • Radius of Gyration • Parallel and Perpendicular Axes Theorems • Moment of Inertia of a Rod, Ring, and Disc • Conservation of Angular Momentum | | 8. Gravitation | • Newton's Law of Gravitation from Kepler's Laws • Acceleration due to Gravity (g = GM/R²) and its Variation with Altitude and Depth • Gravitational Potential Energy • Orbital Velocity and Time Period of a Satellite • Escape Velocity (v e = √(2GM/R)) • Height of Geostationary Satellite | | 9. Mechanical Properties of Solids | • Stress, Strain, and Young's Modulus (Y) • Bulk Modulus and Shear Modulus | | 10. Mechanical Properties of Fluids | • Pascal's Law and its Applications • Equation of Continuity (Av = constant) • Bernoulli's Theorem and its Proof • Torricelli's Law (Velocity of Efflux) • Stokes' Law and Terminal Velocity (v t = 2r²(ρ-σ)g/9η) • Excess Pressure Inside a Liquid Drop and Bubble | | 11. Thermal Properties of Matter | • Linear, Areal, and Volume Thermal Expansion • Thermal Stress • Newton's Law of Cooling | | 12. Thermodynamics | • First Law of Thermodynamics (ΔU = Q - W) • Mayer's Formula (C p - C v = R) • Work Done in Isothermal and Adiabatic Processes • Efficiency of Carnot Engine (η = 1 - T₂/T₁) | | 13. Kinetic Theory | • Pressure Exerted by an Ideal Gas (P = 1/3 ρv²) • Law of Equipartition of Energy and Degrees of Freedom • Root Mean Square (RMS) Speed of Gas Molecules | | 14. Oscillations | • Differential Equation of SHM and its Solution (x = A sin(ωt + φ)) • Expressions for Velocity and Acceleration in SHM • Time Period of SHM for a Spring-Block System (T = 2π√(m/k)) • Time Period of a Simple Pendulum (T = 2π√(L/g)) | | 15. Waves | • The Wave Equation y = A sin(ωt - kx) and its Analysis • Newton's Formula for Speed of Sound in Air and Laplace's Correction • Principle of Superposition, Beats, and Standing Waves • Doppler's Effect in Sound |
W=∫R∞GMmx2dx=GMm[−1x]R∞=GMmRcap W equals integral from cap R to infinity of the fraction with numerator cap G cap M m and denominator x squared end-fraction d x equals cap G cap M m open bracket negative 1 over x end-fraction close bracket sub cap R raised to the infinity power equals the fraction with numerator cap G cap M m and denominator cap R end-fraction This work is supplied as initial kinetic energy:
[v22]uv=a[s]0s⟹v2−u22=as⟹v2=u2+2asopen bracket the fraction with numerator v squared and denominator 2 end-fraction close bracket sub u to the v-th power equals a open bracket s close bracket sub 0 to the s-th power ⟹ the fraction with numerator v squared minus u squared and denominator 2 end-fraction equals a s ⟹ v squared equals u squared plus 2 a s Projectile Motion