Kinematics


   
 
Distance as Area under Velocity-Time Graph
 
The velocity-time graph for uniformly accelerated motion of a particle is illustrated in the figure. Any two points A, B are chosen on the velocity-time graph from which perpendiculars AC, BD, AE, BF are dropped on the time and velocity axes respectively. The coordinates of the points A and B are [t, v(t)] and [tl, v(tl)] respectively.
 
Area included under the position of the AB and the time-axis
 
= area of ACDB = area of rectangle ACDK + area of triangle AKB
 
 
 
 
 
 
 
 
 
 
area ACDB = x (tl) - x (t) which is the distance covered in the time interval (tl - t)
 
The above relationship has been derived by assuming all the variables v(t), v(tl) and 'a' to be positive. However, the same result can be obtained if any or all of the variables are negative.
 
  
     
   
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Kinematics

  		•  Uniform Motion - Introduction
  		• Concept of a Point Object
  		• Rest and Motion
  		• Motion in One, Two and Three Dimensions
  		• Motion in a Straight Line
  		• Position-Time Graph for Non-Uniform Motion
  		• Graphical Representation of Uniform Motion
  		• Uniformly Accelerated Motion - Introduction
  		• Uniformly Accelerated Motion - Introduction
  		• Velocity-Time Graphs of Accelerated Motion
  		• Relations for Uniformly Accelerated Motion (Graphical Treatment)
  		• Position-Time Relations using Position-Time Graphs
  		• Distance as Area under Velocity-Time Graph
  		• Velocity-Time Relations using Calculus
  		• Velocity-Distance Relation
  		• Vectors - Introduction
  		• Definitions
  		• Unit Vector
  		• Fixed Vector
  		• Displacement Vector
  		• Multiplication of Vectors by Real Numbers, i.e., Scalar Multiple of a Vector
  		• Equality of Vectors
  		• The Zero Vector and its Properties
  		• Addition or Composition of Vectors
  		• Parallelogram Law of Vectors
  		• Law of Polygon of Vectors
  		• Resolution and Components of Vectors in a Plane
  		• Dot Product of Vectors and the Resolution of a Vector
  		• Relative Velocity in the Case of Two Velocities Inclined to Each Other
  		• Cross Product or Vector Product of Two Vectors
  		• Motion in a Plane - Introduction
  		• Case of Uniform Velocity
  		• Case of Uniform Acceleration
  		• Expression for Velocity Vector
  		• Projectile Motion
  		• Oblique Projectile
  		• Maximum Height
  		• Uniform Circular Motion
  		• Summary
    Animations
  		• Motion
  		• Difference between Distance and Displacement
  		• S - t Graph or Distance - Time Graph
  		• v - t Graph or Velocity - Time Graph
  		• Speed - Time Graph
  		• Scalar Product and Vector Product of two Vectors
  		• Projectile Motion