The graph between displacement and time for a particle moving with uniform acceleration is a

Options

A. straight line with a positive slope
B. parabola
C. ellipse
D. straight line parallel to time axis

Explanation

To solve the question regarding the graph between displacement and time for a particle moving with uniform acceleration, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**: A particle moving with uniform acceleration means that its velocity is changing at a constant rate. This can be described using the equations of motion.

2. **Use the Equation of Motion**: The equation that relates displacement (s), initial velocity (u), time (t), and acceleration (a) is given by:
\[ s = ut + \frac{1}{2} a t^2 \]

3. **Identify the Terms**: In this equation:
- \(s\) is the displacement,
- \(u\) is the initial velocity,
- \(a\) is the uniform acceleration,
- \(t\) is the time.

4. **Analyze the Equation**: The equation \(s = ut + \frac{1}{2} a t^2\) is a quadratic equation in terms of time \(t\). The term \(ut\) represents a linear relationship, while the term \(\frac{1}{2} a t^2\) introduces a quadratic relationship.

5. **Graphical Representation**: When we plot displacement \(s\) on the y-axis and time \(t\) on the x-axis, the graph will have a quadratic shape due to the \(t^2\) term. This results in a parabolic curve.

6. **Conclusion**: Therefore, the graph between displacement and time for a particle moving with uniform acceleration is a **parabola**.

### Final Answer:
The graph between displacement and time for a particle moving with uniform acceleration is a **parabola**.

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