A graph is a pictorial representation of the relation between two sets of data of which one set is of dependent variables and the other set is of independent variables.
In a displacement-time graph, displacement is a dependent quantity, taken on the Y-axis and time is taken on the X-axis, as it is independent. If the position of an object changes with time, it is said to be in motion. If an object has equal displacements in equal intervals of time then the graph is a straight line inclined with the X-axis which represents uniform motion of the object. If the graph is a curve it represents non-uniform motion. The slope of displacement-time graph gives velocity of the object. However if the graph is a straight line parallel to the X-axis, the object is said to be at rest.
In a velocity-time graph, velocity is a dependent quantity, taken on the Y-axis and time, the independent quantity is taken on the X-axis. If the graph is a straight line parallel to the X-axis then slope of the graph is zero and the object will have uniform velocity, and for uniform velocity the acceleration is zero, instead if the graph is a curve it represents non-uniform velocity and the slope of the graph
gives acceleration of the object. The velocity at any instant of time is called instantaneous velocity. A positive slope of velocity-time graph gives acceleration and a negative slope gives deceleration or retardation of the object. Again if the slope of the velocity-time graph is constant, than the acceleration is termed as uniform acceleration, else if the slope is changing than it is non-uniform acceleration. The area enclosed between the velocity-time graph and time axis gives the displacement of the object. Depending on the velocity, the shape of the area enclosed may be a triangle or a rectangle.
For an object moving with uniform acceleration, we have the following equations of motion,
v = u + at; s= ut +at2 ; v2 - u2 = 2as ;
If an object moves along a straight line path, it is in a linear motion. If an object covers equal angular displacements in equal intervals of time then it is said to be in uniform circular motion. If an object repeats its path again and again after regular intervals of time than it is in periodic motion.