A particle starts moving with constant, velocity `v=2(m)/(s)`, from position `x=5m` The position time graph will be

Options

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Explanation

To solve the problem of finding the position-time graph for a particle moving with a constant velocity, we can follow these steps:

### Step 1: Understand the given information
The particle starts at position \( x = 5 \, \text{m} \) and moves with a constant velocity \( v = 2 \, \text{m/s} \).

### Step 2: Set up the equation of motion
Since the particle is moving with constant velocity, we can use the equation of motion:
\[ x(t) = x_0 + vt \]
where:
- \( x(t) \) is the position at time \( t \),
- \( x_0 \) is the initial position,
- \( v \) is the constant velocity,
- \( t \) is the time.

### Step 3: Substitute the known values
Given that \( x_0 = 5 \, \text{m} \) and \( v = 2 \, \text{m/s} \), we substitute these values into the equation:
\[ x(t) = 5 + 2t \]

### Step 4: Analyze the equation
The equation \( x(t) = 5 + 2t \) is a linear equation in the form \( y = mx + c \), where:
- \( m \) (the slope) is \( 2 \),
- \( c \) (the y-intercept) is \( 5 \).

### Step 5: Draw the graph
1. The y-intercept (where \( t = 0 \)) is at \( x = 5 \, \text{m} \).
2. The slope of the line is \( 2 \), which means for every 1 second that passes, the position increases by \( 2 \, \text{m} \).
3. Thus, the graph will be a straight line starting from the point \( (0, 5) \) and rising with a slope of \( 2 \).

### Step 6: Identify the characteristics of the graph
- The graph is a straight line with a positive slope.
- The line crosses the y-axis at \( 5 \, \text{m} \).

### Conclusion
The position-time graph of the particle is a straight line starting at \( (0, 5) \) and rising with a slope of \( 2 \).