[Following is a text which assumes that the reader is familiar with basics of both Calculus and Vectors.Are Calculus and Vectors important?Believe me if you have good hold on both Calculus and Vectors, all you need is a good book to understand Physics.You can do most of the things yourself]
Kinematics involves problems concerning motion of objects.But, in kinematics we don't take into account the reason for variation in the motion,i.e,we don't use the concepts of Force and Mass to determine the motion.Then how is it determined?
You can know about the motion of a particle by only knowing its position (r) with respect to time (t).If 'r' denotes the position of a particle and 't' denotes time, then, surely 'r' is a function of 't',i.e,'r' depends on 't'.Notice that 'r' is a vector quantity whereas't' is a scalar quantity.
Now,imagine a physical system consisting of a single particle.The position of the particle with respect to a reference frame, at an arbitrary moment in time 't', is determined by the position vector(r) [or radius vector] of the particle. If we introduce the unit vectors i,j,k along the x,y,z axes, respectively, the radius vector r can be represented in the following form
with x(t), y(t) and z(t) as the projection of r(t) along x,y and z axis, respectively.Simultaneously specifying three functions, x(t), y(t) and z(t), is equivalent to specifying a single vector function r(t) of the scalar independent variable 't'.Equation (1.1) is known as the .Thus the law of motion (1.1) specifies the position of the particle at any moment in time.Therefore, determining the motion of a particle quantitatively means finding its law of motion ,i.e, equation (1.1).
The velocity vector and acceleration vector are defined as the appropriate derivative of equation (1.1).Thus:
Equation (1.1) is fundamental to kinematics.Knowing the law of motion,one can determine any parameter of motion. What are parameters of motion? They are the physical quantities characterizing the motion.Mainly acceleration and velocity.
Broadly speaking, problems in kinematics can be classified as direct and indirect[Actually all sorts of problems be it physical or mathematical or... can be classified as direct and indirect.]The direct problem of Kinematics consists in finding any physical quantity characterizing the motion of the particle from the law of motion.In such problems, the law of motion is known or is given in the question itself.It is solved by consistently using the basic laws of kinematics (1.1)- (1.3)
The indirect problem of kinematics consists in determining the law of motion from other parameters of motion(velocity acceleration,etc.).That means anything but equation (1.1) is given and from what is given or known we have to determine equation (1.1).
[Attempt only if you are quite experienced with Calculus and Vectors ]
Can you derive the following equations by concepts discussed here?Suppose the acceleration of the particle is 'a' and remains constant.The velocity at time 0 be 'u' and the velocity at time 't' be ' v'.The particle is moving along the x-axis.
Next post within 10/31/2014.Stay tuned.