Final answer:
The average speed of the object is calculated by finding the difference in its positions at 2.00 s and 3.00 s then dividing by the time interval, resulting in an average speed of 11.00 m/s.
Step-by-step explanation:
The student's question involves finding the average speed of an object moving along the x-axis described by the equation x=3.00t² - 2.00t + 3.00, where x is in meters and t is in seconds. To find the average speed between t=2.00 s and t=3.00 s, one must first calculate the position of the object at these two instances.
Using the given equation, we find:
- x(2.00 s) = 3.00(2.00)² - 2.00(2.00) + 3.00 = 7.00 m
- x(3.00 s) = 3.00(3.00)² - 2.00(3.00) + 3.00 = 18.00 m
The next step is to calculate the total distance traveled, which is the difference in the positions at t=3.00 s and t=2.00 s: Δx = x(3.00 s) - x(2.00 s) = 18.00 m - 7.00 m = 11.00 m. Then, we find the time interval, Δt, which is 1.00 s (3.00-2.00).
Finally, to find the average speed, we divide the total distance traveled by the time interval:
Average Speed = Δx / Δt = 11.00 m / 1.00 s = 11.00 m/s
The average speed of the object between 2.00 s and 3.00 s is thus 11.00 m/s.