Final answer:
To find the average velocity over the time interval [1, 3] for the function d(t) = 2t^2 - 3, evaluate the displacement d(3) - d(1) and divide by the time interval 3 - 1. The average velocity is 8 m/s.
Step-by-step explanation:
The student asks about calculating the average velocity for a given time period for the function d(t) = 2t2 - 3. To find the average velocity between the time interval [1, 3], you need to evaluate the displacement over the time interval and divide it by the total time.
Steps to Calculate Average Velocity:
Calculate the displacement by finding the difference d(3) - d(1).
Calculate the time interval, which is 3 - 1.
Divide the displacement by the time interval to get the average velocity.
Let's perform these steps:
d(3) = 2(3)2 - 3 = 18 - 3 = 15
d(1) = 2(1)2 - 3 = 2 - 3 = -1
Displacement = d(3) - d(1) = 15 - (-1) = 16
Time interval = 3 - 1 = 2 seconds
Average velocity = Displacement / Time interval = 16 / 2 = 8 m/s
Therefore, the average velocity for the time period [1, 3] is 8 meters per second (m/s).