Which is velocity time graph of a moving particle on which net external force is zero

Options

A.
B.
C.
D.

Explanation

To determine which velocity-time (V-t) graph indicates that the net external force acting on a moving particle is zero, we can analyze the characteristics of each graph. Here’s the step-by-step solution:

### Step 1: Understand the relationship between force, mass, and acceleration
According to Newton's second law of motion, the net external force (F_net) acting on an object is given by the equation:
\[ F_{\text{net}} = m \cdot a \]
where:
- \( F_{\text{net}} \) is the net external force,
- \( m \) is the mass of the object,
- \( a \) is the acceleration of the object.

### Step 2: Analyze the velocity-time graph
The slope of a velocity-time graph represents the acceleration of the object. If the slope is zero, it means that the velocity is constant, and thus the acceleration is zero.

### Step 3: Evaluate the options
1. **Option 1**: A horizontal straight line parallel to the time axis.
- This indicates that the velocity is constant over time. Therefore, the acceleration is zero, leading to:
\[ F_{\text{net}} = m \cdot 0 = 0 \]
- This means the net external force is zero.

2. **Option 2**: A line with a positive slope.
- This indicates that the velocity is increasing over time, meaning the acceleration is positive. Thus, there is a non-zero net external force.

3. **Option 3**: A line with a negative slope.
- This indicates that the velocity is decreasing over time, meaning the acceleration is negative. Thus, there is a non-zero net external force.

4. **Option 4**: A vertical line.
- A vertical line implies an infinite rate of change of velocity, which is not physically possible in real scenarios. This would indicate an infinite acceleration and thus an infinite force.

### Step 4: Conclusion
Based on the analysis, the only graph that indicates a net external force of zero is **Option 1**, where the velocity-time graph is a horizontal straight line.

### Final Answer
The correct option is **Option 1**.

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