A particle starts from rest and moves with constant acceleration. Then velocity displacement curve is:

Options

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Answer

To solve the problem of determining the velocity-displacement curve for a particle that starts from rest and moves with constant acceleration, we can follow these steps:

### Step 1: Understand the motion
The particle starts from rest, which means its initial velocity \( u = 0 \). It moves with constant acceleration \( a \).

### Step 2: Use the equations of motion
We can use the third equation of motion, which relates final velocity \( v \), initial velocity \( u \), acceleration \( a \), and displacement \( s \):
\[ v^2 = u^2 + 2as \]
Since the particle starts from rest, we have \( u = 0 \). Therefore, the equation simplifies to:
\[ v^2 = 2as \]

### Step 3: Rearrange the equation
We can rearrange the equation to express \( v \) in terms of \( s \):
\[ v = \sqrt{2as} \]

### Step 4: Analyze the equation
The equation \( v = \sqrt{2as} \) indicates that the velocity \( v \) is proportional to the square root of the displacement \( s \). This relationship suggests that if we plot \( v \) against \( s \), we will get a curve.

### Step 5: Identify the type of curve
The equation \( v^2 = 2as \) represents a parabolic relationship between \( v \) and \( s \). Specifically, it is a parabola that opens upwards, starting from the origin (0,0).

### Step 6: Conclusion
Thus, the velocity-displacement curve for a particle starting from rest and moving with constant acceleration is an upward-facing parabola.

### Final Answer
The velocity-displacement curve is an upward-facing parabola.

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