Draw graph for following equation :
`v=v_(0)-at`

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Answer

To draw the graph for the equation \( v = v_0 - at \), we can follow these steps:

### Step 1: Identify the Variables
In the equation \( v = v_0 - at \):
- \( v \) is the final velocity.
- \( v_0 \) is the initial velocity (y-intercept).
- \( a \) is the acceleration (slope).
- \( t \) is time (x-axis).

### Step 2: Rearrange the Equation
The equation can be rearranged to fit the linear equation format \( y = mx + c \):
- Here, \( v \) (final velocity) corresponds to \( y \).
- \( -a \) (negative acceleration) corresponds to the slope \( m \).
- \( v_0 \) is the y-intercept \( c \).

Thus, we can express it as:
\[ v = -at + v_0 \]

### Step 3: Determine the Intercept and Slope
- **Y-Intercept (\( c \))**: When \( t = 0 \), \( v = v_0 \). This means the graph will intercept the y-axis at \( v_0 \).
- **Slope (\( m \))**: The slope is \( -a \), which is negative if \( a \) is positive. This indicates that as time increases, the velocity decreases.

### Step 4: Plot the Points
1. **Point at \( t = 0 \)**: The point is \( (0, v_0) \).
2. **Point at \( t = t_1 \)**: Choose a value for \( t \) (for example, \( t_1 = \frac{v_0}{a} \)). Then calculate \( v \):
\[ v = v_0 - a \cdot t_1 = v_0 - a \cdot \frac{v_0}{a} = 0 \]
This gives the point \( (t_1, 0) \).

### Step 5: Draw the Graph
- Draw a Cartesian plane with \( t \) on the x-axis and \( v \) on the y-axis.
- Plot the points \( (0, v_0) \) and \( (t_1, 0) \).
- Draw a straight line connecting these two points. The line should slope downwards from left to right, indicating that velocity decreases over time.

### Step 6: Label the Graph
- Label the y-axis as "Velocity (v)" and the x-axis as "Time (t)".
- Indicate the slope as negative and the intercept as \( v_0 \).

### Summary of the Graph
The graph of the equation \( v = v_0 - at \) is a straight line that starts at \( v_0 \) on the y-axis and decreases linearly to zero as time increases, reflecting the negative acceleration.

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