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

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Answer

To solve the problem of determining the displacement-velocity (v) graph of an object moving with uniform acceleration parallel to its instantaneous direction of motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Uniform Acceleration**:
- When an object is moving with uniform acceleration, it means that its acceleration (a) is constant over time. This implies that the change in velocity (v) is uniform.

2. **Relating Displacement and Velocity**:
- The relationship between displacement (s), initial velocity (u), final velocity (v), and acceleration (a) can be described by the equation:
\[ v^2 = u^2 + 2as \]
- Here, \(s\) is the displacement, \(u\) is the initial velocity, and \(v\) is the final velocity.

3. **Graphing Displacement vs. Velocity**:
- Rearranging the equation gives:
\[ s = \frac{v^2 - u^2}{2a} \]
- This equation indicates that displacement (s) is proportional to the square of the velocity (v) when acceleration (a) is constant.

4. **Shape of the Graph**:
- The graph of displacement (s) versus velocity (v) will be a parabola since \(s\) is a quadratic function of \(v\). Specifically, it will open upwards, starting from the point where \(v = u\) (initial velocity).

5. **Conclusion**:
- Therefore, the displacement-velocity graph of the object moving with uniform acceleration parallel to its instantaneous direction of motion is a parabola.