Graphs are mathematical models. They are a very useful way of describing relationships. Graphs are especially useful when describing the motion of the objects, that is, any moving object changes is position with respect to time. The easiest way to describe the motion of a moving body is by using a graph. The most commonly used graphs for describing linear motion of a body are

The geometrical relationship between the distance travelled by an object and the time taken by the object is called the distancetime graph.
The distancetime graph of an object can be drown by taking the time taken along the Xaxis and the distance travelled along the Y axis. The ratio of the distance travelled and the time taken will give the speed of the object. Therefore , the slope of the distancetime graph gives the speed of the given object. That is, by using this graph one can find the speed of an object.
The distancetime graph under different conditions are given below
a) When object is at rest:
At rest the position of the object will be constant, that is the object will not change its position with respect to time. It remains at the same distance at all time. The distancetime graph for an object at rest is a straight line parallel to the time axis. And the slope of the graph will be zero.
b) When object moving with a uniform speed:
When the object covers equal distance in equal interval of time, then said to have a uniform speed. The distancetime graph for object moving with uniform speed is a straight line having all the points falls on it. Which will make an angle with the Xaxis. The slope of the graph will give the speed of an object and the slope must be same everywhere in the straight line.
c) When object moving with nonuniform speed:
When a body moves with nonuniform speed it covers unequal distance in equal intervals of time. The distancetime graph for a body which is moving with nonuniform speed is not a straight line. It is a curve. The speed of the object will change with respect to time.
Displacementtime graph for an object depends upon the nature of motion of the body. Displacement is a vector quantity. It got both direction and magnitude. The slope of a displacementtime graph gives the velocity of the object. The slope of the displacementtime graph is zero when the object is at rest. The displacementtime graph at different conditions say, when the object is at rest, moving with uniform speed and nonuniform speed are given below.
The geometrical relationship between the velocity of an object and the time taken by the object is called the velocitytime graph.
The velocitytime graph of an object can be drown by taking the time taken along the Xaxis and the velocity along the Yaxis. The ratio of the velocity and the time taken will give the acceleration of the object. Therefore, the slope of the velocitytime graph gives the acceleration of the given object. That is, by using this graph one can find the acceleration of an object. The velocitytime graph under different conditions are shown below.
The geometrical relationship between the speed of an object and the time taken by the object is called the speedtime graph. The speedtime graph of an object can be drown by taking the time taken along the Xaxis and the speed along the Yaxis. The ratio of the speed and the time taken will give the acceleration of the object. Therefore, the slope of the speedtime graph gives the acceleration of the given object. That is, by using this graph one can find the acceleration of an object.
The geometrical relationship between the acceleration of an object and the time taken by the object is called the accelerationtime graph. This can be drown by taking the time taken along the Xaxis and the speed along the Y axis.
Accelerationtime graph when the acceleration is constant
Accelerationtime graph when the acceleration is constant
Accelerationtime graph for nonuniform changes
Accelerationtime graph for uniform changes