The position-time graph of a moving particle is a straight line inclined with time axis and passing through origin, therefore

Options

A. Its acceleration is a non-zero constant
B. Its velocity is constant
C. Its displacement is constant
D. Both its velocity and acceleration are changing

Answer

To solve the problem, we need to analyze the position-time graph of a moving particle that is represented as a straight line inclined with the time axis and passing through the origin. Let's break down the solution step by step.

### Step 1: Understand the Graph
The position-time graph is a straight line that passes through the origin. This indicates that the position of the particle is directly proportional to time.

### Step 2: Identify the Slope
In a position-time graph, the slope of the line represents the velocity of the particle. Since the graph is a straight line, the slope is constant.

### Step 3: Determine Velocity
Since the slope is constant, it implies that the velocity of the particle is constant. Mathematically, if we denote position as \( x \) and time as \( t \), the slope (velocity) can be expressed as:
\[ \text{slope} = \frac{dx}{dt} = \text{constant} \]
This means the velocity does not change over time.

### Step 4: Analyze Acceleration
Acceleration is defined as the rate of change of velocity with respect to time. Since we have established that the velocity is constant, it follows that the acceleration must be zero:
\[ a = \frac{dv}{dt} = 0 \]

### Step 5: Evaluate the Given Options
Now, let's evaluate the options provided in the question:
1. **Acceleration is non-zero constant** - This is incorrect, as we found that acceleration is zero.
2. **Velocity is constant** - This is correct, as the slope of the line is constant.
3. **Displacement is constant** - This is incorrect, as the displacement changes with time.
4. **Both velocity and acceleration are changing** - This is incorrect, as velocity is constant and acceleration is zero.

### Conclusion
The only correct option is that the velocity is constant.

### Final Answer
The correct option is: **Velocity is constant.**

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