• Electric Field
  • Gauss' Law
    about below subjects
  • Electric Potential
  • Capacity
  • Direct Current
  • Magnetic Field
  • Magnetic Field Laws
  • Magnetic Interactions
  • Electromagnetic Induction
  • Maxwell's Equations
  • Simple Harmonic Motion
  • Damped Harmonic Motion
  • Driven Harmonic Motion
  • Electric Oscillation
  • Alternating Current
  • Wave Motion
  • Elastic Waves
  • Electromagnetic Waves
  • Light Waves
  • Geometrical Optics
  • Interference
  • Polarization
  • Diffraction
  • Fraunhofer Diffraction
  • Dispersion, Absorption, Diffusion
  • Doppler Effect
  • Ideal Gas
  • Molecular Statistics
  • Transport Phenomena
  • First Law of Thermodynamics
  • Second and Third Laws of Thermodynamics
  • Imperfect Gas
  • Liquids
  • Solids
  • Thermal Radiation
  • Quantum Properties of Light
  • Wave Properties of Particles
  • Planetary Model of Atom
  • X-Rays
  • Particle in Potential Well
  • Pauli Exclusion Principle
  • Nuclear Physics
  • Solid State Physics

Curvilinear Kinematics

SI units & Physics constants


Curvilinear Kinematics investigates lows of motion of objects in space in two and three directions without any reference to forces that cause the motion to change

Curvilinear kinematics quantities

Here (all units see here):

 is original time on time interval

 is final time

 is position vector at time

 is position vector at time

 is displacement vector during time

 is length of path during time

  is mean velocity vector during time

 is instantaneous velocity vector at time , tangent to trajectory

is total acceleration vector at time

are unit vectors of axes x, y, z respectively

General formulas

Displacement vector during time is defined by vector difference


Average velocity vector during time

Instantaneous velocity vector

Average speed during time


Instantaneous speed

Total instantaneous acceleration vector

Relation between acceleration and velocity vectors

Kinematics equation for motion

Relation between curviliner and rectilinear kinematics is defined by vector sum


x(t), y(t), z(t) are coordinates of position vector as functions of time t, defined by rectilinear kinematics

are unit vectors of axes x, y, z shown in the above diagram

Components of total acceleration vector

Components of total acceleration


R is radius of curvature of trajectory at time

is centripetal acceleration, normal to trajectory and directed to its center

is tangential acceleration, tangent to trajectory and parallel to velocity

is total acceleration vector

Magnitude of total acceleration

Angle between vectors  and

Projectile motion

Projectile motion


 is original velocity

 is original angle

is free-fall acceleration directed downward

Kinematic equations for x and y components of position vector:

The x and y components of velocity: