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 ↓


Graphical analysis of motion


Graphical analysis of motion refers to the study and interpretation of graphs that show various aspects of motion. In kinematics, the main focus is on understanding position, velocity, and acceleration, and how they interact over time. Graphs can be a powerful tool for visualizing these relationships and interpreting the underlying motion.

Types of graphs in momentum analysis

There are mainly three types of graphs used in motion analysis:

  • Position-time graph
  • Velocity-time graphs
  • Acceleration-time graphs

Position-time graph

A position-time graph shows how the position of an object changes over time. Position is usually on the vertical axis (y-axis) and time is on the horizontal axis (x-axis).

Consider a simple case where an object moves in a straight line. The position-time graph can tell you:

  • If the object is stationary (the line is horizontal).
  • If the object is moving with a constant velocity (the line is straight but not horizontal).
  • If the object is accelerating (the line is curved).

Examples: constant velocity

Time Position (Male)

In this example, we see a straight line, which represents constant velocity. The steeper the line, the greater the velocity.

Mathematically, velocity can be found using the slope of the line:

velocity = Δposition / Δtime

Examples: acceleration

When an object is accelerating, the shape of the graph is a curve.

Time Position (Male)

This curved line shows that the object is accelerating. The steeper the curve, the greater the acceleration.

Velocity-time graphs

Velocity-time graphs show the velocity of an object over time. These graphs can tell you:

  • If the object is stationary (the line is on the horizontal axis).
  • If the object is moving with a constant velocity (the line is horizontal above or below the x-axis).
  • If the object is accelerating (the line has a slope).

Examples: constant velocity

Time Velocity (m/s)

In this example, the horizontal line represents constant velocity. The value of velocity is the height of the line above the x-axis.

Example: constant acceleration

If the object is accelerating, the velocity-time graph will be a straight line with a slope.

Time Velocity (m/s)

This straight, non-horizontal line indicates that the object is undergoing constant acceleration. The slope of the line can be used to find the acceleration:

acceleration = Δvelocity / Δtime

The area under the velocity-time graph represents the displacement of the object during that time interval.

Acceleration-time graphs

An acceleration-time graph shows how an object's acceleration changes over time. Unlike the other two types of graphs, acceleration-time graphs usually provide information about changes in speed rather than specific details about position or velocity.

Constant acceleration

Time Acceleration (m/s²)

A horizontal line on an acceleration-time graph represents constant acceleration. If this line is at zero, the object is not accelerating.

Momentum analysis through graphs

Using graphs, we can gain important information about the motion of an object. Let's see how we can analyze and interpret these graphs.

From position-time to velocity

The slope of the position-time graph at any point gives the velocity of the object at that instant. If the slope is positive, the object is moving forward, while a negative slope indicates backward motion.

From velocity-time to displacement

The area under the line in the velocity-time graph gives the displacement of the object. It can be calculated by finding the area of geometric shapes like triangles and rectangles under the graph line.

Example: calculating displacement

Consider a velocity-time graph in which a line forms a triangle above the x-axis. The base (time) of the triangle is 5 seconds, and the height (velocity) is 10 m/s. Displacement can be calculated as:

displacement = ½ × base × height = ½ × 5 × 10 = 25 meters

From velocity-time to acceleration

The slope of the velocity-time graph shows the acceleration of the object. The greater the slope, the greater the acceleration.

Practical example

Below are some practical examples that bring together the concepts of position-time and velocity-time graphs.

Example 1: A car accelerating from rest

Consider a car starting from rest and accelerating uniformly:

The position-time graph is initially flat and gradually slopes upward, indicating increasing velocity. The velocity-time graph of the car will be a straight sloping line, indicating constant acceleration.

Example 2: Bouncing ball

Consider a ball that is dropped from a height, bounces back up, and then falls back down:

In the position-time graph, the peaks represent the maximum height of the ball during each bounce. The valleys represent when the ball hits the ground.

Conclusion

Graphical analysis of motion is a fundamental tool for understanding how objects move. By interpreting position-time, velocity-time, and acceleration-time graphs, we can gain more in-depth information about motion. Whether constant velocity, constant acceleration, or complex motion, these graphs provide a visual and quantitative way to comprehensively analyze and understand various aspects of motion.


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Graphical analysis of motion

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