To determine the position of the object after it completes the motion described in the velocity vs. time graph, we need to calculate the displacement at each time interval and sum them up.

The velocity-time graph is piecewise linear, and the area under the curve in each interval represents the displacement during that interval.

1. Interval 0 to 2 seconds:

   • Velocity = 50 m/s
   • Time = 2 s
   • Displacement = $50 \, \text{m/s} \times 2 \, \text{s} = 100 \, \text{m}$

2. Interval 2 to 6 seconds:

   • Velocity changes from 50 m/s to 40 m/s, forming a trapezoid.
   • Average velocity = $\frac{50 + 40}{2} = 45 \, \text{m/s}$
   • Time = 4 s
   • Displacement = $45 \, \text{m/s} \times 4 \, \text{s} = 180 \, \text{m}$

3. Interval 6 to 8 seconds:

   • Velocity changes from 40 m/s to 30 m/s, forming a trapezoid.
   • Average velocity = $\frac{40 + 30}{2} = 35 \, \text{m/s}$
   • Time = 2 s
   • Displacement = $35 \, \text{m/s} \times 2 \, \text{s} = 70 \, \text{m}$

4. Interval 8 to 10 seconds:

   • Velocity changes from 30 m/s to 10 m/s, forming a trapezoid.
   • Average velocity = $\frac{30 + 10}{2} = 20 \, \text{m/s}$
   • Time = 2 s
   • Displacement = $20 \, \text{m/s} \times 2 \, \text{s} = 40 \, \text{m}$

Now, sum the displacements:

$100 \, \text{m} + 180 \, \text{m} + 70 \, \text{m} + 40 \, \text{m} = 390 \, \text{m}$

Finally, add this to the initial position of the object:

$20 \, \text{m} + 390 \, \text{m} = 410 \, \text{m}$

The position of the object after it completes the motion is 410 meters to the north.

Please let me know if you want more details or have any questions.

Questions you might ask:

1. Can you explain the calculation for each interval in more detail?
2. How do you determine the area under a velocity-time graph?
3. What is the significance of the initial position in this problem?
4. How does the average velocity calculation work for trapezoidal sections?
5. Can you show the step-by-step process for one of the intervals?

Tip:

When analyzing a velocity-time graph, remember that the area under the curve represents the displacement of the object.