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 ↓


Motion in one dimension


Motion is a part of our everyday lives. Whenever we look around, we see things that move. From the falling of an apple to the complex movements of vehicles, motion is everywhere and is fundamental to physics. In this topic, we will explore "motion in one dimension", which is the simplest form of motion.

Let's first understand what "motion" means. Motion refers to the change in the position of an object with respect to time and its surrounding environment. When we discuss motion in one dimension, we refer to motion along a straight line.

Post

Let us first define the position of an object. Position is a point in space that is defined relative to a reference point. It is usually described using a coordinate system such as a number line.

0 1 2 3 4

In the diagram above, the line represents the path an object can take. The numbers are positions on this path, with 0 being the reference point. If an object is at position 2, it means it is 2 units away from the reference point.

Distance and displacement

When discussing motion, it's important to distinguish between distance and displacement. Distance is the total path length traveled by an object, regardless of its initial or final position. Displacement, on the other hand, is the change in an object's position. It's a vector quantity, which means it has both magnitude and direction.

Example: If you walk 3 m towards east and then 4 m towards west, the total distance travelled will be 7 m. However, the displacement will be 1 m towards west.

Speed and velocity

Another important aspect of motion is speed. Speed is the speed that shows the speed of an object, calculated as the distance traveled per unit of time. It is a scalar quantity and does not include direction.

Speed = Distance / Time

However, velocity is a vector quantity. It tells the rate at which an object changes its position. It includes both speed and direction.

Velocity = Displacement / Time

Example: If you walked 100 meters north in 10 seconds, your speed is 10 m/s and your velocity is 10 m/s north.

Start Ending Displacement

Acceleration

Acceleration is the rate of change of an object's velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction.

Acceleration = Change in Velocity / Time

If the speed of a car changes from 20 m/s to 30 m/s in 5 sec, then the acceleration will be:

Acceleration = (30 m/s - 20 m/s) / 5 s = 2 m/s²

Acceleration can be positive or negative. Positive acceleration is often referred to as speeding up, while negative acceleration (or deceleration) means slowing down.

t = 0s T = TS Start Ending

Kinematic equations

To describe motion in one dimension, we often use a set of kinematic equations. These equations relate displacement, initial velocity, final velocity, acceleration, and time:

  1. v = u + at
  2. S = UT + 0.5AT²
  3. v² = u² + 2as

Where:

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

These equations are powerful tools for predicting the future position and velocity of moving objects.

Example problem: A car accelerates from rest at a constant rate of 3 m/s² for 10 seconds. What is its final velocity and how much distance does it travel?

Using the first equation: v = u + at = 0 + 3 * 10 = 30 m/s Using the second equation: s = ut + 0.5at² = 0 + 0.5 * 3 * 100 = 150 meters

The car reaches a final velocity of 30 m/s and travels a distance of 150 m.

Graphical representation of motion

Motion can also be represented using graphs of position versus time, velocity versus time, and acceleration versus time.

Position versus time graph: This graph shows how the position of an object changes over time. The slope of the line on this graph gives the velocity.

Time Post

Velocity vs. Time Graph: This graph shows how velocity changes over time. The slope of this graph represents acceleration, and the area under the curve represents displacement.

Time Velocity

Applications and examples

Motion in one dimension is not just a theoretical concept but is also used in real life. Let's look at some examples:

Example 1: Falling objects
Objects in free fall move with a constant acceleration due to gravity, which is about 9.8 m/s². If you drop a ball from a building, you can use the equations of motion to predict how long it will take to fall to the ground.

Example 2: A car travels straight on a highway
Cars often travel in straight lines on highways, making them a classic example of one-dimensional motion. Knowing the initial speed and acceleration, you can predict the car's future position and speed.

Conclusion

Motion in one dimension provides a fundamental understanding of how objects move in a straight line. By learning concepts such as position, distance, displacement, speed, velocity, and acceleration, and using kinematic equations, you can efficiently analyze and predict the motion of objects.

Whether you are following the trajectory of a thrown ball or the motion of vehicles on the road, mastering one-dimensional motion is important for further exploration of more complex motion in two and three dimensions.


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Motion in one dimension

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