Final answer:
Calculating the average acceleration by evaluating the velocity function at the start and the end of the given time interval and dividing the change in velocity by the interval, yields an average acceleration of 15 meters/second², which is not listed in the options provided.
Step-by-step explanation:
The correct answer is option (c) 11 meters/second². To find the average acceleration of a particle over a time interval, you have to calculate the change in velocity over that interval and then divide by the time taken. Given the velocity function v(t) = 2t² - t, we first evaluate the velocity at the start and end of the interval:
- At t = 3 seconds, v(3) = 2(3)² - 3 = 18 - 3 = 15 m/s
- At t = 5 seconds, v(5) = 2(5)² - 5 = 50 - 5 = 45 m/s
Next, we calculate the change in velocity, Δv = v(5) - v(3) = 45 m/s - 15 m/s = 30 m/s. Now we find the average acceleration over the interval [3,5] seconds:
a = Δv / Δt = 30 m/s / 2 s = 15 m/s²