The task asks to determine the distance traveled by a body in the time interval from $t = 0$ to $t = 5$ seconds, based on the graph of its velocity $v_x$ over time $t$.

Key Concepts:

• The graph provided is a velocity-time graph, and the area under the curve within a certain time interval represents the displacement (if areas are taken with signs) or the total distance traveled (if areas are taken as absolute values).
• The distance is obtained by summing the absolute values of the areas under the velocity curve over the time interval.

Step-by-Step Solution:

From $t = 0$ to $t = 5$, the velocity graph can be broken into distinct shapes (rectangles and triangles), and we will calculate the area of each.

1. From $t = 0$ to $t = 2$:

   • This forms a triangle with a base of $2$ seconds and a height of $10 \, \text{m/s}$.
   • Area of triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 10 = 10 \, \text{m}$.

2. From $t = 2$ to $t = 4$:

   • This forms a triangle with a base of $2$ seconds and a height of $-10 \, \text{m/s}$ (negative because it's below the time axis).
   • The area (displacement) = $\frac{1}{2} \times 2 \times 10 = 10 \, \text{m}$ (absolute value is taken to calculate distance).

3. From $t = 4$ to $t = 5$:

   • This forms a small rectangle with a base of $1$ second and a height of $5 \, \text{m/s}$.
   • Area of rectangle = $1 \times 5 = 5 \, \text{m}$.

Total Distance:

The total distance traveled is the sum of the absolute values of the areas: $\text{Distance} = 10 \, \text{m} + 10 \, \text{m} + 5 \, \text{m} = 25 \, \text{m}$

Thus, the distance traveled from $t = 0$ to $t = 5$ seconds is 25 meters.

Would you like any further explanation or details on any of the steps?

Here are 5 related questions:

1. How would the result change if the velocity graph included negative areas (representing opposite direction)?
2. What would be the displacement from $t = 0$ to $t = 5$ seconds?
3. How is displacement different from total distance traveled?
4. How do you calculate the area under a curve in more complex velocity-time graphs?
5. How does constant acceleration affect the velocity-time graph?

Tip: Always take care to differentiate between distance and displacement when dealing with velocity-time graphs. Distance is always positive, but displacement can be negative.