Grade 9
  1. Mechanics  1.1. Motion  1.1.1. Types of motion  1.1.2. Distance and displacement  1.1.3. Speed and Velocity  1.1.4. Acceleration  1.1.5. Graphical representation of motion  1.1.6. Equations of motion  1.1.7. Uniform and non-uniform motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Relative speed  1.1.10. Circular motion  1.2. Laws of force and motion  1.2.1. The concept of force  1.2.2. newton's first law of motion  1.2.3. Newton's second law of motion  1.2.4. Newton's third law of motion  1.2.5. Inertia and types of inertia  1.2.6. Motion  1.2.7. Conservation of momentum  1.2.8. Application of Newton's laws in daily life  1.2.9. Types of Forces (Contact and Non-Contact)  1.2.10. Friction and its effects  1.3. Gravitational force  1.3.1. Newton's law of universal gravitation  1.3.2. Importance of Gravitational Force  1.3.3. Acceleration due to gravity  1.3.4. Free fall and weightlessness  1.3.5. Mass and weight  1.3.6. Variation of g with height and depth  1.3.7. Kepler's laws of planetary motion  1.3.8. Satellites and their orbits  1.4. Work, Energy and Power  1.4.1. Concept of work  1.4.2. Positive and negative actions  1.4.3. Work done by constant and variable force  1.4.4. Energy and its forms  1.4.5. Kinetic energy and potential energy  1.4.6. Law of conservation of energy  1.4.8. Commercial unit of energy  1.4.9. Work–energy theorem  1.5. Simple machines  1.5.1. Types of simple machines  1.5.2. Mechanical advantage  1.5.3. Machine efficiency  1.5.4. Levers and their types  1.5.5. Pulleys and Inclined Planes  1.5.6. Gears and their uses
  2. Properties of matter  2.1. States of matter  2.1.1. Solids, liquids and gases  2.1.2. Properties of different states of matter  2.1.3. Change in state of matter  2.1.4. Plasma and Bose–Einstein condensate  2.2. Density and pressure  2.2.1. Concept of density and relative density  2.2.2. Pressure in solids, liquids and gases  2.2.3. Pascal's law and its applications  2.2.4. Atmospheric pressure and its variations  2.2.5. Surface tension and capillarity  2.3. Buoyancy and Archimedes' principle  2.3.1. Buoyant force  2.3.2. Archimedes principle  2.3.3. Applications of Archimedes' Principle  2.3.4. floating and sinking objects  2.3.5. Theory of Flotation and Archimedes' Principle
  3. Heat and Thermodynamics  3.1. Temperature and heat  3.1.1. Concept of heat and temperature  3.1.2. Temperature measurement  3.1.3. Temperature scales  3.2. Heat transfer  3.2.1. Conduction of heat  3.2.2. Convection of heat  3.2.3. heat radiation  3.2.4. Applications of heat transfer  3.2.5. Thermal conductivity  3.3. Thermal expansion  3.3.1. Expansion of solids, liquids and gases  3.3.2. Abnormal expansion of water  3.3.3. Applications of Thermal Expansion  3.4. Specific heat capacity and latent heat  3.4.1. Concept of specific heat capacity  3.4.2. Measurement and applications of specific heat  3.4.3. Latent heat of fusion and vaporization  3.4.4. Heat Engines and Efficiency
  4. Waves and sound  4.1. Waves and their types  4.1.1. Mechanical and electromagnetic waves  4.1.2. Longitudinal and Transverse Waves  4.1.3. Properties of Waves  4.1.4. Wavelength, frequency and speed of the wave  4.1.5. Superimposition of waves  4.2. Sound waves  4.2.1. Nature and transmission of sound  4.2.2. Speed of sound in different mediums  4.2.3. Reflection of sound and echo  4.2.4. Sonar and ultrasound  4.2.5. Resonance and pulsation  4.3. Sound characteristics  4.3.1. Intensity, loudness and quality of sound  4.3.2. Doppler effect in sound
  5. Lighting and Optics  5.1. Reflection of light  5.1.1. Laws of reflection  5.1.2. Reflection from a plane mirror  5.1.3. Reflection from a spherical mirror  5.1.4. Image formation by concave and convex mirrors  5.1.5. Applications of Reflection  5.2. Refraction of light  5.2.1. Laws of refraction  5.2.2. Refractive index  5.2.3. Refraction through a glass slab  5.2.4. Refraction in water and air  5.2.5. Lenses and their types  5.2.6. Image formation by convex and concave lenses  5.2.7. Total internal reflection and its applications  5.3. Dispersion and scattering of light  5.3.1. Spectrum of white light  5.3.2. Prisms and Dispersion  5.3.3. Tyndall effect and blue sky
  6. Electricity and Magnetism  6.1. Electric charge and static electricity  6.1.1. The concept of electric charge  6.1.2. Charging by friction, contact and induction  6.1.3. Electroscope and its working  6.2. Current Electricity  6.2.1. The concept of electric current  6.2.2. Ohm's Law and Resistance  6.2.3. Factors affecting resistance  6.2.4. Series and Parallel Circuits  6.2.5. Heating effect of electric current  6.2.6. Electric power and energy  6.3. Magnetism  6.3.1. Natural and artificial magnets  6.3.2. Properties of magnets  6.3.3. Earth's magnetism  6.3.4. Magnetic field and field lines  6.3.5. Electromagnets and their applications
  7. Modern Physics  7.1. structure of the atom  7.1.1. Atomic Structure and Subatomic Particles  7.1.2. Electrons, Protons, and Neutrons  7.1.3. Rutherford and Bohr model  7.2. Radioactivity  7.2.1. Types of radioactive emissions  7.2.2. Half-life and radioactive decay  7.2.3. Uses and Hazards of Radioactivity
  8. Space science and astronomy  8.1. The universe and its components  8.1.1. Stars and galaxies  8.1.2. Planets and Solar System  8.2. Satellites  8.2.1. Natural and artificial satellites  8.2.2. Use of satellites

Grade 9 → Mechanics → Motion ↓


Relative speed


Relative speed is a fundamental concept in physics, which helps us understand how objects move relative to each other. This concept is essential in analyzing various physical scenarios and plays a vital role in the perception of speed in our daily lives.

Basic concepts of relative motion

In mechanics, when we discuss the motion of objects, we often describe their motion relative to something else. Relative motion is the calculation of the motion of an object in relation to another moving or stationary object. It is important for understanding a variety of phenomena, from simple exercises like running on a treadmill to more complex phenomena like predicting the orbits of planets.

Frames of reference

To understand relative motion, we first need to introduce the idea of a frame of reference. The frame of reference is simply the viewpoint from which motion is observed and measured. For example, when you stand on the sidewalk and watch a car go by, your reference frame is the Earth.

Example of a reference frame

Suppose a person is sitting in a train moving in the north direction at a speed of 100 km/h. Suppose an observer sitting on the ground (outside the train) sees a passenger inside the train moving in the south direction at a speed of 5 km/h. How do we describe the motion of the passenger?

  • From the point of view of the observer on the ground (ground frame of reference): The passenger is moving north at a speed of 95 km/h (100 km/h for the train - 5 km/h for the pedestrian).
  • From the passenger's point of view (train's reference frame): The passenger is moving south at a speed of 5 km/h.

Relative velocity

Relative velocity is the velocity of an object as seen from a particular frame of reference. If two objects are moving in different directions or at different speeds, their relative velocity will be different depending on the reference frame chosen.

        Relative velocity of object A with respect to object B: V AB = V A - V B
        Relative velocity of object A with respect to object B: V AB = V A - V B

Example of relative velocity

Consider two cars moving on a straight road: car A is moving east at a speed of 60 km/h and car B is moving east at a speed of 40 km/h. To find the velocity of car A relative to car B, we use the formula:

        V AB = V A - V B = 60 km/h - 40 km/h = 20 km/h
        V AB = V A - V B = 60 km/h - 40 km/h = 20 km/h

This means that car A appears to be moving at a speed of 20 km/h in the east direction relative to car B.

Direction matters in relative motion

Direction is important in understanding the concept of relative speed. The velocity vector of an object not only tells us how fast the object is moving, but also the direction in which it is moving. Therefore, it is necessary to consider the direction when calculating relative velocities.

Directional example

Imagine two people swimming in a river:

  • Swimmer A is moving upstream at a speed of 2 m/s relative to the bank of the river.
  • Swimmer B is moving downstream at a speed of 3 m/s relative to the bank of the river.

The formula to find the relative velocity of swimmer B with respect to swimmer A would be:

        V BA = V B - V A = 3 m/s - (-2 m/s) = 3 m/s + 2 m/s = 5 m/s
        V BA = V B - V A = 3 m/s - (-2 m/s) = 3 m/s + 2 m/s = 5 m/s

This result shows that swimmer B moves downstream at a speed of 5 m/s relative to swimmer A.

Graphical representation of relative motion

Relative motion can also be represented through simple graphical displays to aid understanding. Consider two points, A and B, each representing an observer or object, such as two people or a car. The lines and arrows represent their relative motion.

A B Velocity of B with respect to A

In this SVG diagram, the lines represent motion paths, where the line from A to B (in black) represents the velocity of A, and the longer line (in red) represents the speed of B relative to A.

Practical examples of relative motion

Let's look at some everyday scenarios where relative momentum plays a key role:

Example 1: Moving paths

At airports, moving walkways help passengers move faster. Consider a passenger moving at 3 km/h on a moving walkway that is itself moving at 2 km/h in the same direction. From the perspective of a stationary observer, the passenger appears to be moving at this speed:

        Total velocity = Walk speed + Walkway speed = 3 km/h + 2 km/h = 5 km/h
        Total velocity = Walk speed + Walkway speed = 3 km/h + 2 km/h = 5 km/h

However, if the traveler decides to walk in the opposite direction of the walkway:

        Total velocity = Walk speed - Walkway speed = 3 km/h - 2 km/h = 1 km/h
        Total velocity = Walk speed - Walkway speed = 3 km/h - 2 km/h = 1 km/h

Example 2: A ship at sea

Two ships sailing at sea may be moving in opposite directions. Understanding their relative speeds is important to avoid collision.

If ship A is moving due north at a speed of 20 km/h and ship B is moving due south at a speed of 15 km/h, then what is the relative velocity of ship A with respect to ship B?

        V AB = V A - (-V B ) = 20 km/h + 15 km/h = 35 km/h
        V AB = V A - (-V B ) = 20 km/h + 15 km/h = 35 km/h

A deeper understanding of relative motion from a mathematical perspective

As mentioned, measuring relative velocity involves subtracting vectors, but understanding it mathematically can make the concept more concrete.

Vectors and their part in relative motion

Velocity and displacement are vector quantities; they have magnitude and direction. When measuring relative motion, especially relative velocity, operations on vectors become necessary.

Addition and subtraction of vectors

Relative speed is determined by the difference of vectors. Consider a more advanced scenario in which one airplane flies east at 500 km/h and another flies northeast at 300 km/h from the same point. To determine the relative speed, vector subtraction will provide the velocity of the second plane relative to the first.

Importance and applications

Relative speed is not just an academic concept; it affects our daily lives and many fields such as transportation, aviation and even astronomy. Pilots, drivers and ship captains all use the principles of relative speed to navigate safely and efficiently.

Astronomical applications

Relative motion allows astronomers to predict the movements of planets, stars, and galaxies. By measuring the relative motion of these celestial bodies to one another, scientists can understand the dynamics of the solar system and beyond.

Conclusion

Relative speed helps us understand how we perceive the motion of objects in relation to each other. Understanding frames of reference and vectors makes the principles of relative velocity clearer. This understanding plays a vital role in real-world applications, whether it is simple traffic navigation or complex celestial mechanics.


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Relative speed

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