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**Hint:**Here the graph is drawn with velocity square along the x axis and displacement along the y axis. The tangent to the angle made by the line with the x axis gives the slope of the straight line. Using the ${v^2}$ versus $s$ graph, write the equation of a line and compare it to the kinematic equation. By comparing we will be able to tell about its acceleration, initial acceleration.

**Formula used:**

$y = mx + c$

Where y is the value where the line cuts y axis.

${v^2} = {u^2} + 2as$

Where $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, $s$ is the displacement.

**Complete step by step solution:**

Graphical analysis is a convenient method to study the motion of studying the motion of a particle. The motion situation of a particle can be effectively analysed by graphical representation.

For graphical representation, we require two coordinate axes. The usual practice is to take the independent variable along the x axis and dependent variable along the y axis.

First from the graph ${v^2}$ versus $s$ let us write the line equation:

${v^2} = cs + {c_1}$

Where $c$ and ${c_1}$ are constants

Kinematic equation of motion

${v^2} = 2as + {u^2}$

Comparing the two equations we can say the acceleration is uniform.

Since acceleration is uniform, we can $s \propto {t^2}$. Hence $s - t$ graph will be a parabola.

If $s = 0$ in the equation ${v^2} = cs + {c_1}$, we get ${v^2} = {c_1}$ from this we can say that initial velocity is not zero.

**Hence option $\left( B \right)$ is the right option.**

**Note:**The tangent to the angle made along the x axis gives the slope of the straight line. The motion situation of a particle can be effectively analysed by graphical representation. Graphical analysis can be effectively applied to analyse the motion situation of a particle. A graph can be drawn by using the two coordinates one along the x axis and one along the y axis. Here the x axis contains an independent variable.

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