If velocity v varies with time(t) as `v=2t-3`, then the plot between v and t is best represented by :

Options

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Answer

To solve the problem of plotting the relationship between velocity \( v \) and time \( t \) given by the equation \( v = 2t - 3 \), we can follow these steps:

### Step 1: Identify the Equation
The equation given is:
\[ v = 2t - 3 \]
This is a linear equation in the form of \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept.

### Step 2: Determine the Slope and Intercept
From the equation \( v = 2t - 3 \):
- The slope \( m \) is \( 2 \).
- The y-intercept \( c \) is \( -3 \).

### Step 3: Plot the Intercept
On a graph where the y-axis represents velocity \( v \) and the x-axis represents time \( t \):
- The y-intercept is at \( (0, -3) \). This means when \( t = 0 \), \( v = -3 \).

### Step 4: Determine Another Point
To draw the line, we can find another point by substituting a value for \( t \). Let's choose \( t = 3 \):
\[ v = 2(3) - 3 = 6 - 3 = 3 \]
So, another point is \( (3, 3) \).

### Step 5: Draw the Line
Now we can plot the points \( (0, -3) \) and \( (3, 3) \) on the graph. Since the slope is positive, the line will rise as it moves from left to right. Draw a straight line through these points, which will extend in both directions.

### Step 6: Analyze the Graph
The line will cross the y-axis at \( -3 \) and will have a positive slope, indicating that as time \( t \) increases, the velocity \( v \) also increases.

### Conclusion
The plot between \( v \) and \( t \) will be a straight line that starts below the origin (at \( -3 \)) and rises to the right.

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