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 ↓


Acceleration and deceleration


Dynamics is a branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. Two fundamental aspects of motion are acceleration and deceleration, which describe how the velocity of an object changes with time.

Understanding acceleration

Acceleration is defined as the rate of change of an object's velocity. It is a vector quantity, which means it has both magnitude and direction. When something gets faster, we say it is accelerating.

Acceleration formula

Acceleration can be calculated using the following formula:

acceleration = (final velocity - initial velocity) / time

Where:

  • final velocity is the velocity of the object at the end of the time period
  • initial velocity is the velocity of the object at the beginning of the time period
  • time is the period during which the change occurs

Visual example of acceleration

Consider a car that starts from stationary and increases its speed while traveling on a straight road. For the sake of clarity I will present this example using code rather than an image.

|Time (s)| Velocity (m/s) | Acceleration (m/s²)|
-----------------------------------------------
| 0      | 0              | 0                  |
| 1      | 5              | 5                  |
| 2      | 10             | 5                  |
| 3      | 15             | 5                  |

As time passes, the velocity of the car increases by 5 m/s every second, resulting in a constant acceleration of 5 m/s².

Example problem

Imagine that a sports car accelerates from stationary to 60 m/s in 10 seconds. What is the acceleration of the car?

Using the acceleration formula:

acceleration = (60 m/s - 0 m/s) / 10 s = 6 m/s²

So, the acceleration of the car is 6 m/s².

Understanding recessions

Deceleration is the rate at which an object slows down. It is essentially negative acceleration. When an object is slowing down, its velocity decreases over time.

Bearish formula

This formula is similar to the acceleration formula, but the change in velocity will be a negative number because the object is slowing down:

deceleration = (final velocity - initial velocity) / time

Visual example of a recession

Let's imagine that the bicycle stops after applying the brake. Again, let's illustrate this example in the form of a table:

|Time (s)| Velocity (m/s) | Deceleration (m/s²)|
-----------------------------------------------
| 0      | 20             | -4                 |
| 1      | 16             | -4                 |
| 2      | 12             | -4                 |
| 3      | 8              | -4                 |
| 4      | 4              | -4                 |
| 5      | 0              | -4                 |

The bicycle is slowing down at 4 m/s every second, so its constant deceleration rate is -4 m/s².

Example problem

A train moves at a speed of 30 m/s and stops in 15 seconds. Calculate the speed of the train.

Using the dilution formula:

deceleration = (0 m/s - 30 m/s) / 15 s = -2 m/s²

The deceleration speed of the train is -2 m/s².

Real-life applications

Acceleration and deceleration can be seen in many real-life situations, including:

  • Vehicles: Cars, buses, trains and planes all accelerate and decelerate constantly.
  • Game: Players increase speed when they start the race and decrease speed when they stop.
  • Amusement rides: Roller coasters continually increase and decrease speed throughout the ride.

Key points to remember

  • Both acceleration and deceleration are vector quantities, that is, they have direction and magnitude.
  • Acceleration results in an increase in velocity, while deceleration results in a decrease in velocity.
  • The formulas for both are similar, yet the direction of the velocity change determines whether an object is accelerating or decelerating.

Advanced ideas

Although this text provides a basic understanding, higher level physics can explore the following:

  • Non-uniform acceleration: When the acceleration is not constant, calculus techniques can be used to describe the changing state.
  • Vector representation: In more advanced physics, acceleration is broken down into components using vector mathematics.
  • Relativity of Acceleration: The effects of acceleration on objects at high speeds can be explored from the point of view of relativity.

Conclusion

Acceleration and deceleration are fundamental concepts in physics that describe how the velocity of an object changes over time. Understanding these principles is important for analyzing motion in everyday life, whether you're looking at a speeding car, a child on a swing, or a satellite orbiting the Earth.

This broad introduction gives you the tools you need to think about how motion occurs, and lays the groundwork for more complex studies in physics.


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Acceleration and deceleration

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