An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The dispalcement (s)-velocity (v) graph of this object is.

Options

A.
B.
C.
D.

Explanation

To solve the problem of finding the displacement (s) - velocity (v) graph for an object moving with uniform acceleration in the direction of its motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**:
The object is moving with uniform acceleration (A) in the direction of its initial velocity (u). We need to analyze the relationship between displacement (s) and velocity (v).

2. **Use the Kinematic Equation**:
We can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:
\[ v^2 = u^2 + 2as \]
Here, \(u\) is the initial velocity, \(v\) is the final velocity, \(a\) is the uniform acceleration, and \(s\) is the displacement.

3. **Assume Initial Conditions**:
For simplicity, let’s assume the initial velocity \(u = 0\). This means the equation simplifies to:
\[ v^2 = 2as \]

4. **Rearranging the Equation**:
Rearranging the equation gives us:
\[ s = \frac{v^2}{2a} \]
This shows that displacement \(s\) is proportional to the square of the velocity \(v\).

5. **Identify the Graph Type**:
The equation \(s = \frac{1}{2a} v^2\) is in the form of a quadratic equation, which represents a parabola. Specifically, it indicates that as \(v\) increases, \(s\) increases quadratically.

6. **Graph Characteristics**:
Since \(s\) is plotted on the y-axis and \(v\) on the x-axis, the graph will be an upward-facing parabola starting from the origin (0,0).

7. **Conclusion**:
Thus, the displacement-velocity graph for the object moving with uniform acceleration is an upward-facing parabola.

### Final Answer:
The displacement (s) - velocity (v) graph of the object is an upward-facing parabola.