To find the total distance traveled by the vehicle, we need to calculate the area under the velocity-time graph over the given 16-minute period. The graph is divided into two sections: a triangle from 0 to 10 minutes and another triangle from 10 to 16 minutes.

Step-by-Step Solution

1. First Triangle (0 to 10 minutes):

   • Base = 10 minutes
   • Height = 7 m/s
   • Area = $\frac{1}{2} \times \text{base} \times \text{height}$ $= \frac{1}{2} \times 10 \times 7 = 35 \, \text{meters}$

2. Second Triangle (10 to 16 minutes):

   • Base = 6 minutes
   • Height = 7 m/s
   • Area = $\frac{1}{2} \times \text{base} \times \text{height}$ $= \frac{1}{2} \times 6 \times 7 = 21 \, \text{meters}$

Total Distance

Adding the areas of both triangles: $35 + 21 = 56 \, \text{meters}$

Answer

The total distance traveled by the vehicle is 56.00 meters (to 2 decimal places).

Would you like further details or have any questions?

Here are some related questions:

1. How do you interpret velocity-time graphs for different types of motion?
2. Why is the area under a velocity-time graph equal to the distance traveled?
3. How would the calculation change if there were a curve instead of straight lines?
4. What does a negative slope on a velocity-time graph indicate?
5. How do you convert units if the time were in seconds instead of minutes?

Tip: When calculating distance from a velocity-time graph, always look for areas under the curve, as this represents the total distance.