A particle starting from rest moves along a straight line with constant acceleration for this velocity displacement graph will have the form-

Options

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Answer

To solve the problem of determining the form of the velocity-displacement graph for a particle starting from rest and moving with constant acceleration, we can follow these steps:

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

**Hint:** Remember that "starting from rest" means the initial velocity is zero.

### Step 2: Use the kinematic equation
For a particle moving with constant acceleration, we can use the kinematic equation that relates velocity (v), initial velocity (u), acceleration (a), and displacement (s):
\[ v^2 = u^2 + 2as \]
Since the initial velocity \( u = 0 \), the equation simplifies to:
\[ v^2 = 2as \]

**Hint:** Identify the variables in the equation: \( v \) is the final velocity, \( a \) is acceleration, and \( s \) is displacement.

### Step 3: Rearranging the equation
From the equation \( v^2 = 2as \), we can express \( s \) in terms of \( v \):
\[ s = \frac{v^2}{2a} \]
This shows that displacement \( s \) is proportional to the square of the velocity \( v^2 \).

**Hint:** Look for the relationship between \( s \) and \( v \) to determine the shape of the graph.

### Step 4: Identify the type of graph
The equation \( s = \frac{1}{2a} v^2 \) indicates that \( s \) is proportional to \( v^2 \). This means that if we plot \( v^2 \) on the y-axis against \( s \) on the x-axis, we will get a straight line. However, if we plot \( v \) against \( s \), the graph will be parabolic because \( s \) is proportional to \( v^2 \).

**Hint:** Consider how the graph would look if you plotted \( v \) against \( s \) based on the relationship derived.

### Step 5: Conclusion
Since the velocity \( v \) is related to the displacement \( s \) by a quadratic relationship, the velocity-displacement graph will be parabolic.

Thus, the correct answer is that the velocity-displacement graph will have the form of a **parabola**.

**Final Answer:** The velocity-displacement graph will be parabolic.

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