Kinematics


   
 
Acceleration
Definition
 
The acceleration of a moving point is the rate of change of its velocity. Note that the acceleration of a moving object is a vector, as it has both magnitude and direction.
 
The acceleration is uniform when equal changes of velocity take place in equal intervals of time, in the same direction, however small these intervals may be.
 
 
In CGS system, it is measured in cms-2, while in SI, it is measured in ms-2.
 
Negative acceleration is called retardation or deceleration.
 
Average acceleration
Average acceleration is the ratio of the change in velocity to the time taken to undergo this change.
 
 
 
Let a particle move along a straight line OL, as shown in the figure above. Let the particle be at the origin O at t = 0.
 
Let A and B be the positions of the particle at times t1 and t2 respectively.
 
Let (v) t1 and (v) t2 be the magnitudes of the respective velocities. Then, the magnitude of average acceleration is given by,
 
 
 
Instantaneous acceleration
Instantaneous acceleration is the acceleration at any instant of time or at any given point.
 
The limiting value of the average acceleration as Dt tends to zero, is called instantaneous velocity.
 
 
Variable acceleration
A particle is said to move with variable acceleration if its velocity changes by unequal amounts in equal intervals of time.
 
When a particle moves with variable acceleration, then its average acceleration measured for different time intervals is not the same. In the case of variable acceleration, the acceleration can vary in magnitude or in direction or both.
 
  
     
   
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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