Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Mechanics → Dynamics ↓


Acceleration


Dynamics is a branch of physics that describes the motion of objects. One of the main components of dynamics is acceleration. In simple terms, acceleration refers to the rate at which an object changes its velocity. It is not only how fast an object is moving, but also how quickly it is changing its speed or direction.

What is acceleration?

Acceleration is a vector quantity, which means it has both magnitude and direction. The unit of acceleration in the International System of Units (SI) is meters per second squared (m/s2). Acceleration can be positive (speeding up) or negative (slowing down), sometimes referred to as deceleration or retardation.

Acceleration formula

The formula for calculating acceleration is:

a = (v_f - v_i) / t

Where:

  • a is the acceleration
  • v_f is the final velocity
  • v_i is the initial velocity
  • t is the time taken in the change of velocity

Illustration through example

Consider a car that accelerates from 0 m/s to 20 m/s in 5 seconds. To find the acceleration of the car, substitute the values in the formula:

a = (20 m/s - 0 m/s) / 5s = 4 m/s2

This means that the velocity of the car increases by 4 metres per second every second.

Initial speed = 0 m/s Final speed = 20 m/s Time = 5 sec

Types of acceleration

1. Uniform acceleration

Uniform acceleration occurs when an object changes its velocity by the same amount every equal period of time. For example, if a car increases its velocity by 2 m/s every second, its acceleration is uniform.

2. Uneven acceleration

Non-uniform acceleration occurs when the change in velocity is not the same over equal intervals of time. For example, if a car accelerates at different rates every second, it experiences non-uniform acceleration.

Graphical representation of acceleration

In dynamics, speed graphs are an essential tool for understanding acceleration. Let's take a look at some of the ways these graphs depict motion:

1. Velocity-time graph

The velocity-time graph is a straightforward way to represent acceleration. The slope of the line on a velocity-time graph represents acceleration.

Time Velocity (m/s) Constant acceleration

In this graph, the red line represents constant positive acceleration. The straight, diagonal line means that the speed increases at a constant rate.

Real life examples of acceleration

Example 1: Acceleration in a roller coaster

Roller coasters are thrilling because they have very rapid changes in acceleration. As the roller coaster travels down its track, gravity causes it to speed up rapidly. Imagine a roller coaster starting from stationary and reaching a speed of 24 m/s in 4 seconds:

a = (24 m/s - 0 m/s) / 4s = 6 m/s2

It is this rapid acceleration that creates a feeling of excitement and speed.

Example 2: Car braking

When the driver applies the brakes, the car experiences negative acceleration or deceleration. For example, if a car traveling at 30 m/s stops in 5 seconds:

a = (0 m/s - 30 m/s) / 5s = -6 m/s2

This shows that the car is slowing down at the rate of 6 meters per square second.

Equations of speed and acceleration

To understand acceleration, it is also important to master the equations of motion. These equations help calculate the unknown variables of motion, provided the other variables are known.

1. The first equation of motion

v = u + at

Where:

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

2. The second equation of motion

s = ut + 1/2at^2

Where:

  • s is the displacement
  • u is the initial velocity
  • t is the time
  • a is the acceleration

3. The third equation of motion

v^2 = u^2 + 2as

Where:

  • v is the final velocity
  • u is the initial velocity
  • s is the displacement
  • a is the acceleration

Example: Applying the equations of motion

If a car starts from rest and accelerates at 3 m/s2 for 8 seconds, find the final velocity and total displacement.

Using the first equation of motion:

v = u + at = 0 + (3 m/s^2 * 8 s) = 24 m/s

Using the second equation of motion:

s = ut + 1/2at^2 = 0 + 1/2(3 m/s^2)(8 s)^2 = 96 m

Thus, the car reaches a velocity of 24 m/s and covers a displacement of 96 m.

Factors affecting acceleration

Various factors can affect the acceleration of an object, such as:

  • Force: According to Newton's second law, the acceleration of an object is directly proportional to the net force acting on it.
  • Mass: The acceleration of an object is inversely proportional to its mass if the net force remains constant.
  • Friction: Acts opposite to the direction of motion, often reducing acceleration.

Conclusion

Acceleration is a fundamental concept in dynamics and physics. Understanding acceleration helps to understand how objects move and change speed in real-world scenarios. Mathematical and graphical methods provide clarity to this concept, which is applicable in many fields such as transportation, sports, and various technological advancements.


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Acceleration

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