**Finding Total Velocity using the Velocity-Time Graph**

To find the total velocity from a velocity-time graph, we need to understand the relationship between velocity and time. The velocity-time graph represents the variation of velocity with respect to time. The slope of the graph at any point represents the instantaneous velocity at that particular time.

To find the total velocity, we can add the slopes of different intervals on the velocity-time graph. By breaking down the graph into smaller intervals and calculating the slopes of each interval, we can determine the total velocity.

**Step-by-Step Process:**

1. **Break Down the Graph**: Start by breaking down the velocity-time graph into smaller intervals. These intervals can be of equal or varying durations, depending on the given data.

2. **Calculate the Slope**: For each interval, calculate the slope of the line connecting the two points that define the interval. The slope can be determined by dividing the change in velocity by the change in time.

3. **Sum the Slopes**: Add up the slopes obtained from each interval. This will give us the total velocity.

4. **Interpret the Result**: The total velocity obtained represents the overall change in velocity over the given time period.

**Example:**

Let's consider an example to understand this concept better:

Suppose we have a velocity-time graph with two intervals:

- Interval 1: From time t=0s to t=5s, with a slope of 2 m/s²
- Interval 2: From time t=5s to t=10s, with a slope of -3 m/s²

To find the total velocity, we add the slopes:

Total velocity = slope of Interval 1 + slope of Interval 2
= 2 m/s² + (-3 m/s²)
= -1 m/s²

Therefore, the total velocity over the given time period is -1 m/s².

**Conclusion:**

In conclusion, we can find the total velocity by adding the slopes of different intervals on the velocity-time graph. By breaking down the graph into smaller intervals, calculating the slopes for each interval, and summing them up, we can determine the overall change in velocity over the given time period. This method allows us to analyze the velocity-time graph and determine the total velocity accurately.