Final answer:
The average velocity of the particle from time t = 1 to t = 3, with the velocity function v(t) = 2 - t^2, is calculated by integrating the velocity function over the time interval and dividing by the total time. The result of the integration is -5 - 2/3, and after dividing by the total time of 2 seconds, the average velocity is (Option c) -7/3 m/s.
Step-by-step explanation:
The question asks to calculate the average velocity of a particle moving along the x-axis with a velocity function v(t) = 2 - t2 from time t = 1 to t = 3. To find the average velocity, we need to calculate the total displacement over the time period and divide it by the total time.
The total displacement can be found by integrating the velocity function from t = 1 to t = 3:
∫ v(t) dt from 1 to 3 = ∫ (2 - t2) dt from 1 to 3
This gives us:
(2t - t3/3) | from 1 to 3 = (2(3) - 33/3) - (2(1) - 13/3) = 6 - 9 - 2 + 1/3 = -5 - 2/3
The total time is 3 - 1 = 2 seconds. Hence, the average velocity = (-5 - 2/3) / 2 = -7/3 m/s.
Therefore, the correct answer is (Option c). -7/3.