The graphs provide a convenient method to present pictorially, the basic informations about a variety of events. Line graphs are used to show the relation of one quantity say displacement or velocity with another quantity such as time.
If the displacement, velocity and acceleration of a particle are plotted with respect to time, they are known as,

*Graphical representations*

The graphs provide a convenient method to
present pictorially, the basic informations about a variety of events. Line
graphs are used to show the relation of one quantity say displacement or
velocity with another quantity such as time.

If the displacement, velocity and acceleration
of a particle are plotted with respect to time, they are known as,

1. displacement ? time graph (*s - t* graph)

2. velocity ? time graph (*v - t* graph)

3. acceleration ? time graph (*a - t* graph)

**Displacement ? time graph **

When the displacement
of the particle is plotted as a function of time, it is displacement - time graph.

As v = ds/dt , the slope of the s - t graph at
any instant gives the velocity of the particle at that instant. In Fig. 2.4 the
particle at time t1, has a positive velocity, at time t2, has zero velocity and
at time t3, has negative velocity.

**Velocity
? time graph**

When the velocity of the particle is plotted as
a function of time, it is velocity-time graph.

As a = dv/dt , the slope of the v ? t curve at
any instant gives the acceleration of the particle (Fig. 2.5).

But v=ds/dt or

Ds = v dt

If the displacements are s_{1} and s_{2
}in times t_{1} and t_{2} then

∫_{1}^{2}ds = ∫_{ t1}^{t2}
vdt

S_{2}-s_{1} = ∫_{t1}^{t2}vdt
= area ABCD

The area under the v ? t curve, between the
given intervals of time, gives the change in displacement or the distance
travelled by the particle during the same interval.

**Acceleration
? time graph**

When the acceleration is plotted as a function
of time, it is acceleration ? time graph (Fig. 2.6).

A=dv/dt

Or dv = adt

If the velocities are v_{1} and v_{2}
at times t_{1} and t_{2} respectively, then

∫_{v1}^{v2} dv = ∫_{t1}^{t2}
a dt

V_{2}-v_{1} = ∫_{t1}^{t2}adt
= area PQRS

The area under the a ? t curve, between the
given intervals of time, gives the change in velocity of the particle during
the same interval. If the graph is parallel to the time axis, the body moves
with constant

acceleration.

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