Step 1 :Given the points on the graph, we can see that the runner's velocity is increasing linearly from 0 to 12 m/s over the first 4 seconds.
Step 2 :The average velocity is calculated by the total displacement divided by the total time.
Step 3 :The total displacement can be calculated as the area under the velocity-time graph, which forms a trapezoid in this case.
Step 4 :The formula for the area of a trapezoid is \((\text{base1} + \text{base2}) / 2 * \text{height}\). Here, base1 is the initial velocity (0 m/s), base2 is the final velocity (12 m/s), and the height is the time interval (4 s).
Step 5 :Calculate the total displacement: \(\text{displacement} = (0 + 12) / 2 * 4 = 24.0\) m
Step 6 :Calculate the average velocity: \(\text{average_velocity} = \text{displacement} / \text{time} = 24.0 / 4 = 6.0\) m/s
Step 7 :Final Answer: The average velocity for the first 4 seconds is \(\boxed{6 \, \mathrm{m/s}}\).