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 ↓


Speed and Velocity


In physics, dynamics is the branch that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause the motion. This study focuses on two fundamental concepts: speed and velocity. Both are essential to describing and understanding motion.

What is speed?

Speed is a scalar quantity that represents the "speed of an object". It is the rate at which an object covers a distance. Average speed is calculated by dividing the total distance covered by the total time taken to cover that distance. The formula for speed is very simple:

Speed = Distance / Time

For example, if a car travels 150 kilometers in 3 hours, then its speed will be:

Speed = 150 km / 3 hours = 50 km/h

Visual example of motion

Start finish object moving at a constant speed

In the SVG example above, a red circle moves from the start to the finish line. Speed represents how fast the circle moves from the start to the finish point in a given time.

What is velocity?

On the other hand, velocity is a vector quantity that refers to the "rate at which an object changes its position". Unlike speed, velocity includes the direction of the object. Thus, velocity is more informative about the object's state of motion. Average velocity is calculated by dividing the displacement by the time during which the change occurred.

Velocity = Displacement / Time

Consider a car that travels 100 km east in 2 hours. Its velocity will be:

Velocity = 100 km east / 2 hours = 50 km/h east

Visual example of velocity

A B C velocity is towards B

In this SVG, a blue circle moves from point A to point B, indicating the direction of its velocity. It is important to understand that even though the object continues to move toward point C, the velocity is only defined from point A to B.

Difference between speed and velocity

Although both speed and velocity provide information about the movement of an object, they have some important differences:

  • Speed is a scalar quantity, which means it has only magnitude. While velocity is a vector quantity, which means it has both magnitude and direction.
  • Speed does not give any information about the direction of travel. Velocity provides clear directional information.
  • The velocity of an object moving at a constant speed on a circular path keeps changing because its direction keeps changing continuously.

Text examples for practice

Example 1: Calculating speed

If a cyclist covers a distance of 60 km in 2 hours, what is the speed of the cyclist?

Speed = Distance / Time = 60 km / 2 hours = 30 km/h

Example 2: Calculating velocity

A runner moving towards north covers a distance of 400 m in 50 seconds. What is the velocity of the runner?

Velocity = Displacement / Time = 400 meters north / 50 seconds = 8 m/s north

Example 3: Spotting the difference

A car travels 100 km in the north direction and then 100 km in the east direction. What are distance, speed, displacement and velocity?

  • Distance = 100 km + 100 km = 200 km
  • Speed = Total distance / Total time
  • Displacement: Use Pythagoras theorem (√(100² + 100²) = 141.42 km) towards North-East direction.
  • Velocity = Displacement / Time

Understanding instantaneous speed and velocity

While average speed and velocity are calculated over a certain amount of time, instantaneous speed and velocity refer to these quantities at a specific moment. Imagine you are driving and glancing at your speedometer, which reads the speed of your car at that exact moment - this is your instantaneous speed.

Instantaneous Speed = Lim Δt → 0 (Δs/Δt)

Since velocity also considers direction, the instantaneous velocity will specify the direction of motion at that particular instant.

Visual analogy: comparing escalators and stairs

A B

In the above analogy, consider lines going upward to represent two people - one using the escalator and the other using the stairs. The person on the escalator (left line) reaches the top faster; therefore, their speed is greater. However, if both eventually move in the same upward direction, their velocities will be equal but different in magnitude. Remarkably, the speed for the escalator remains constant, while the stairs may involve instantaneous speed changes.

Connecting speed and velocity with a graph

In many physics problems, interpreting graphs is important to understand speed and velocity. The most common graphs are distance-time and velocity-time graphs.

Distance-time diagram

In a distance versus time graph, speed is represented by the slope of the graph. A steeper slope indicates greater speed. A flat, horizontal line does not represent any speed, because distance does not change over time.

Velocity-time graphs

On a velocity-versus-time graph, constant velocity is shown as a horizontal line, and the slope (gradient) of the line represents acceleration. Calculating the area under the line between two time intervals gives displacement.

Conclusion

Understanding momentum and velocity is the foundational knowledge for further study in physics and mechanics. These concepts are important in analyzing and predicting the motion of objects in everyday life - from vehicles on roads to athletes in competitions. Mastery of momentum and velocity principles also aids in understanding more complex phenomena and systems in advanced physics.


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Speed and Velocity

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