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 determine the graph between displacement and time for a particle moving with uniform acceleration, we can follow these steps:

### Step 1: Understand the motion
A particle moving with uniform acceleration means that its acceleration (a) is constant over time. This affects how its displacement (x) changes with time (t).

### Step 2: Use the equation of motion
The equation of motion that relates displacement, initial velocity, time, and acceleration is given by:
\[ x = u t + \frac{1}{2} a t^2 \]
Where:
- \( x \) is the displacement,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.

### Step 3: Analyze the case of starting from rest
If the particle starts from rest, the initial velocity \( u = 0 \). Thus, the equation simplifies to:
\[ x = \frac{1}{2} a t^2 \]

### Step 4: Identify the relationship
This equation shows that displacement \( x \) is proportional to the square of time \( t^2 \) when acceleration \( a \) is constant. This indicates a parabolic relationship.

### Step 5: Graph the relationship
- If acceleration \( a \) is positive, the graph of \( x \) versus \( t \) will be a parabola opening upwards.
- If acceleration \( a \) is negative, the graph will still be a parabola but opening downwards.

### Step 6: Conclusion
The graph between displacement and time for a particle moving with uniform acceleration is a parabola.