Motion in One Dimension

Syllabus for Motion in One Dimension

  • Core Concepts: The curriculum covers scalar and vector quantities, distance, speed, velocity, and acceleration.
  • Graphical Representation: Study includes graphs of distance-time and speed-time (velocity-time) and the specific information that can be derived from these graphical representations.
  • Motion Types: Focus is restricted to rest and motion in one dimension, including motion under gravity.
  • Acceleration Constraints: The syllabus focuses on uniformly accelerated motion. Non-uniform acceleration is explicitly excluded.
  • Equations of Motion: Derivation and application of the following equations for uniformly accelerated motion (to be derived graphically):
    • v=u+atv = u + at
    • S=ut+12at2S = ut + \frac{1}{2}at^{2}
    • S=(u+v)t2S = \frac{(u + v)t}{2}
    • v2=u2+2aSv^{2} = u^{2} + 2aS
  • Problem Solving: Simple numerical problems related to the above concepts and equations.

Classification of Physical Quantities

  • Definition: Physical quantities are defined as quantities that can be measured.
  • Broad Categories: They are classified into two main categories: scalar quantities (scalars) and vector quantities (vectors).

Scalar Quantities (Scalars)

  • Definition: Scalar quantities are physical quantities that are completely expressed by their magnitude only.
  • Parameters for Expression: Two parameters are required to express a scalar quantity completely:
    • Numerical Value: The actual number of the measured quantity.
    • Unit: The unit in which the quantity is being measured.
  • Pure Numbers: If a scalar is a pure number, such as π\pi or e2e^{2}, it possesses no unit.
  • Examples of Scalar Quantities:
    • Mass, length, time, distance, density, volume, and speed.
    • Temperature and potential (including gravitational, magnetic, and electric potential).
    • Work, energy, power, pressure, electrical power, and quantity of heat.
    • Specific heat, electric charge, resistance, and density.
    • Mechanical advantage, frequency, and angle.
  • Mathematical Operations: Scalars can be added, subtracted, multiplied, and divided using simple arithmetic methods.
  • Symbolic Representation: Usually represented by a standard English letter. Examples include:
    • Mass: mm
    • Time: tt
    • Speed: vv

Vector Quantities (Vectors)

  • Definition: Physical quantities that require both magnitude and direction to provide complete meaning. Magnitude alone is insufficient.
    • Metaphor/Scenario: If instructed to "displace a particle from a point by 5 m5\,m", the logical follow-up question is "in which direction?" For the meaning to be complete, a direction such as "towards east" must be specified.
  • Parameters for Expression: Three parameters are required to express a vector quantity completely:
    • Numerical Value of the quantity.
    • Unit.
    • Direction.
  • Magnitude Characteristics: The magnitude is the numerical value of the vector quantity combined with its unit and is always a positive value.
  • The Negative Sign: In vector notation, a negative sign indicates the reverse or opposite direction. For example, the forces F⃗\vec{F} and −F⃗-\vec{F} act in opposite directions.
  • Examples of Vector Quantities:
    • Displacement, velocity, and acceleration.
    • Momentum, force, and impulse.
    • Weight and moment of a force (torque).
    • Magnetic field, electric field, temperature gradient, and dipole moment.
  • Mathematical Operations: Vectors do not follow simple arithmetic; they require different algebraic rules for addition, subtraction, and multiplication.
  • Symbolic Representation: Vector quantities are generally written as an English letter with an arrow above it or in bold typeface. Examples:
    • Velocity: v⃗\vec{v} or v\mathbf{v}
    • Acceleration: a⃗\vec{a} or a\mathbf{a}
    • Force: F⃗\vec{F} or F\mathbf{F}