Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Mechanics → dynamics ↓


Relative velocity in one and two dimensions


The concept of velocity is very important to understand in physics, especially when considering the motion of objects relative to one another. In dynamics, relative velocity describes how fast one object is moving compared to another object. It can be analyzed in one dimension or two dimensions.

Relative velocity in one dimension

Let's start with the simplest case: motion in a straight line. When two objects are moving in the same or opposite directions, calculating the relative velocity involves determining how fast one object is moving relative to the other.

Basics of relative velocity

Suppose you have two objects, A and B, moving on the same road. If A has a velocity v A and B has a velocity v B, then the relative velocity of A relative to B is given by:

V AB = V A - V B

Here, v AB represents how fast A is moving compared to B.

Example

Example 1: Two cars are on the highway. Car A is traveling at 60 km/h, and car B is traveling in the same direction at 40 km/h. What is the velocity of car A relative to car B?

Use of the formula:

V AB = V A - V B

v AB = 60 km/h - 40 km/h = 20 km/h

Hence car A is moving at a speed of 20 km/h relative to car B.

Example 2: Suppose a person is walking on a train. The train is moving east at 30 m/s, and the person inside the train is moving west at 2 m/s. What is their velocity relative to an observer standing outside?

v person = v train + v w = 30 m/s - 2 m/s = 28 m/s (Ex)

Visual example

A B

In the above scene, the red circle represents car A and the blue circle represents car B, both moving on the same straight path.

Relative velocity in two dimensions

When moving in two dimensions, the motion occurs along both the x and y axes. Calculating the relative velocity becomes more complicated because it involves vector subtraction.

Vector representation

In two dimensions, the velocity of an object is represented as a vector:

v = v x î + v y ĵ

Here, v x is the velocity component in the x-direction and v y is the velocity component in the y-direction.

Calculating relative velocity

Let the velocity of two objects A and B be:

v A = v A x î + v A y ĵ
v b = v bx î + v by ĵ

The relative velocity v AB of A with respect to B is the vector subtraction:

v AB = (v Ax – v Bx) î + (v Ay – v By) ĵ

Example

Example 3: Two airplanes are flying. Airplane A is traveling at 300 m/s (60° north of east), and airplane B is traveling east at 200 m/s. What is the velocity of A relative to B?

First, analyze the velocity of airplane A:

v axis = 300 * cos(60°) = 150 m/s
v y = 300 * sin(60°) = 259.8 m/s

Velocity of plane B:

v bx = 200 m/s
v by = 0 m/s

The relative velocity is:

V AB = (150 - 200) î + (259.8 - 0) ĵ = (-50) î + 259.8 ĵ m/s

Visual example

A B

In the above visualization, plane A is traveling along the green vector and plane B is traveling along the orange vector. Subtracting the vectors gives the relative velocity vector.

Key points to remember

  • The concept of relative velocity allows us to describe the motion of an object with respect to another reference object.
  • In one dimension, the relative velocity is straightforward and involves simple subtraction.
  • In two dimensions, this requires an understanding of basic trigonometry for vector subtraction and vector decomposition.
  • Understanding relative speed is essential in understanding motion in various real-life scenarios such as navigation, aviation, and physics.

With practice, solving problems involving relative velocity becomes effortless and lays a solid foundation for further study in physics.


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Relative velocity in one and two dimensions

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