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 ↓


Equations of motion


In physics, specifically mechanics, the "equations of motion" are fundamental principles that describe how objects move. These equations allow us to predict the future position and velocity of moving objects. Let's learn what these equations are and how we can use them to better understand motion.

The basics of speed

Motion means the change in position of an object over time. In everyday life, you see motion everywhere: a ball rolling down a hill, a car moving down the road, or a plane flying in the sky. In physics, we usually describe motion like this:

  • Location: The place where the object is located.
  • Velocity: How fast and in what direction an object is moving.
  • Acceleration: How the velocity of an object changes with time.

Three equations of motion

There are three main equations of motion that relate to these concepts. These equations assume that the acceleration of the object is constant. This simplification allows us to accurately estimate the motion. The equations are as follows:

First equation of motion

The first equation relates initial velocity, final velocity, acceleration and time. It is expressed as:

v = u + at

Where:

  • v is the final velocity
  • u is the initial velocity
  • a is the acceleration
  • t is the time

Imagine you are riding a bicycle. You start from rest, so your initial velocity is 0. As you pedal faster, your speed increases. If you pedal with constant acceleration for a certain amount of time, where will you be? This equation helps you find your velocity after that amount of time.

Example: Suppose you throw a ball straight up with an initial velocity of 10 m/s², and it is subject to a gravitational acceleration of -9.8 m/s² (negative because gravity acts downward). After 2 seconds, what is its velocity?

v = 10 m/s + (-9.8 m/s²) * 2 s
v = 10 m/s - 19.6 m/s
v = -9.6 m/s

After 2 seconds, the velocity of the ball will be -9.6 m/s, which means it is moving downward.

Second equation of motion

The second equation gives the position of the object. This relation is as follows:

s = ut + (1/2)at²

Where:

  • s is the displacement
  • u, a, and t are as defined before

This equation helps you find out how much distance you have travelled. Think of it like this: how much distance the car has travelled after starting from rest and then accelerating for some time.

Example: Suppose you drop a stone from the top of a tower. If it starts at rest (initial velocity is 0) and the acceleration due to gravity is -9.8 m/s², how far will it fall in 3 seconds?

s = 0 * 3 s + 0.5 * (-9.8 m/s²) * (3 s)²
s = 0 - 0.5 * 9.8 m/s² * 9
s = -44.1 m

The negative sign indicates that the rock fell 44.1 m.

rock

This picture shows a rock falling down from a tower.

Third equation of motion

The third equation relates velocity, acceleration, and displacement, leaving out time. It is expressed as:

v² = u² + 2as

This equation is useful when you need to solve for displacement without knowing how long it took. It also helps determine how fast an object might be moving at a given displacement.

Example: Imagine an arrow is thrown upward with an initial velocity of 15 m/s. Find how high it will travel until it stops (when the final velocity is 0), assuming a uniform gravitational acceleration of -9.8 m/s² acts on it.

0 = (15 m/s)² + 2 * (-9.8 m/s²) * s
0 = 225 m²/s² - 19.6 m/s² * s
19.6 m/s² * s = 225 m²/s²
s = 225 m²/s² / 19.6 m/s²
s = 11.48 m

Therefore, the arrow will rise about 11.48 meters from its starting point and then pause for a moment before falling back down.

Visual understanding of motion with SVG

Visualizing motion can help clarify these concepts. The following simple diagram shows an object first moving steadily and then accelerating.

Start Constant speed Acceleration Ending

The blue dot represents the initial position. The green and yellow dots represent constant speed, where the interval remains the same over time. The red dot represents the increased distance due to acceleration.

Practical applications

Understanding and applying the equations of motion helps solve many real-world problems. For example, engineers use these principles to design vehicle braking distances, athletes use them to improve their performance, and astronomers calculate the trajectories of spacecraft.

For example, if an engineer wants to design a new roller coaster, they must ensure the cars have enough velocity at the top of the loop, calculate the g-forces acting on the riders, and more. Using the equations of motion will guide them in performing these calculations safely and accurately.

Conclusion

Equations of motion are essential tools in physics for describing and predicting the motion of objects. By understanding the initial velocity, acceleration, and time, one can find the position and velocity of objects in motion.

These equations not only provide a solid foundation for more advanced studies in physics but also have practical applications in various fields, which help us understand the role of physics in our daily lives.


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Equations of motion

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