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 ↓


Acceleration


Acceleration is a fundamental concept in physics that describes how the velocity of an object changes over time. It is a vector quantity, meaning it has both magnitude and direction. In this lesson, we will explore the concept of acceleration in detail using simple English, multiple examples, and visual explanations.

What is acceleration?

To understand acceleration, we first need to understand velocity. Velocity is the speed of something in a certain direction. For example, if a car is moving east at 60 kilometers per hour (km/h), that is its velocity.

Now, acceleration occurs when there is a change in velocity. This change can be an increase or decrease in speed, a change in direction, or both. For example, if the car mentioned earlier speeds up to 80 km/h, slows down to 40 km/h, or turns north while maintaining speed, it is accelerating in all of these scenarios.

Types of acceleration

There are mainly three scenarios where acceleration occurs:

  • Positive acceleration: This occurs when an object increases speed. For example, when a car starts from a rest position at a traffic light and gains speed, it is experiencing positive acceleration.
  • Negative acceleration or deceleration: This occurs when an object slows down. Using the example of a car, when it approaches a stop sign and begins to slow down, the car slows down.
  • Change in direction: Even if the speed remains constant, if an object changes its direction, it is accelerating. Consider a car that is moving at a constant speed on a circular track. Although the speed does not change, the direction keeps changing constantly, thus the car is accelerating.

Acceleration formula

Mathematically, acceleration is calculated by dividing the change in velocity by the time during which the change occurs. The formula for calculating acceleration is:

a = (v_f - v_i) / t

Where:

  • a = acceleration
  • v_f = final velocity
  • v_i = initial velocity
  • t = time period during which the change occurs

Units of acceleration

The standard unit of acceleration is meters per second squared (m/s 2), but it can also be expressed in other units, such as kilometers per hour squared. This depends on which units are used for velocity and time.

Visual example 1: Linearly accelerating car

Let's imagine how acceleration works when a car's speed increases. Imagine a car starts at zero velocity and accelerates in a straight line:

Step 1: v_i = 0 m/s, t = 0 s --> the car is at rest.
Step 2: After 1 second, v_f = 3 m/s.
Step 3: After 2 seconds, v_f = 6 m/s.
The car is increasing in speed by 3 m/s every second.
        
        
        Car path

In this example, the acceleration is constant, and you could say that the car's acceleration is 3 m/s2.

Lesson example 1: Throwing a ball upwards

Consider throwing a ball straight up in the air. Let's break it down into parts:

  1. Initial throw: The ball moves away from your hand at a high positive velocity when you apply upward force.
  2. In the middle: The ball slows down until it stops at the peak. Here the velocity is zero, and it starts moving backwards.
  3. Landing: The ball accelerates toward the ground, increasing speed as it descends until it is caught or hits the ground.

As the ball rises, there is a constant negative acceleration due to gravity (known as the gravitational acceleration, which is about 9.81 m/s 2 toward the Earth). As the ball falls, the ball accelerates in the opposite direction at the same rate.

Visual example 2: Cyclist taking a turn

        
        
        
        Diversion path

Imagine a cyclist moving at a constant speed but turning around in a circular turn. Although the speed remains the same, the direction changes, which represents a change in the velocity vector. This is an example of centripetal acceleration, which is necessary to change direction while keeping the speed constant.

Text example 2: Stopping the bus

Let us consider a bus traveling at a speed of 20 meters per second (20 m/s) that begins to reduce its speed to stop at a bus stop:

  1. The initial speed is 20 m/s.
  2. As it applies brakes, the velocity gradually decreases to 15 m/s, 10 m/s, 5 m/s, and finally to 0 m/s.

Here, the bus experiences negative acceleration when it slows down. The acceleration value will be negative, which represents the decrease in speed over time until the bus stops.

The role of acceleration in everyday life

Acceleration is not just a concept in physics, but it plays an important role in everyday experiences. Here are some scenarios:

  • When you press the accelerator pedal of a car, the speed of the vehicle increases.
  • Braking produces negative acceleration, which slows down the vehicle.
  • Roller coasters provide thrilling experiences by rapidly changing velocity and direction, and exhibit both positive and negative acceleration.

Acceleration problems

Let's solve a simple problem to understand acceleration better:

Problem: A skateboarder starts from rest and reaches a speed of 10 m/s in 5 seconds. What is his acceleration?

Solution:

        v_i = 0 m/s (initial velocity), v_f = 10 m/s (final velocity), t = 5 s
a = (v_f - v_i) / t
a = (10 m/s - 0 m/s) / 5 s
a = 2 m/s 2

The skateboarder accelerates at a rate of 2 meters per second squared.

Conclusion

Acceleration is a fundamental aspect of motion within physics, essential for understanding how the velocity of objects changes over time. Whether it's cars moving on roads, athletes sprinting, or celestial bodies moving through space, acceleration plays a vital role. By understanding the types, equations, and real-life contexts, you can better understand how dynamic our world is.


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Acceleration

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