An object moves along a straight path. Its position, S, in meters, at t seconds, is given by s(t)= 2t^2-t/t-1. Determine the average rate of change of the object after 3s/
1. 29/16 m/s
2. 5/16 m/s
3. 5/4 m/s
4. 29/4 m/s
since having t/t is kind of dumb, I suspect you meant
s(t) = (2t^2-t)/(t-1). If so, then
(s(3)-s(0))/(3-0) = (15/2 - 0)/3 = 5/2
Hmmm. Maybe you can fix it.
To determine the average rate of change of the object after 3 seconds, we need to find the difference in the object's position at 3 seconds and at some earlier time. Let's calculate it step by step:
Step 1: Find the position of the object at 3 seconds.
Plug in t = 3 into the equation s(t) = (2t^2 - t) / (t - 1):
s(3) = (2(3)^2 - 3) / (3 - 1)
s(3) = (2(9) - 3) / 2
s(3) = (18 - 3) / 2
s(3) = 15 / 2
s(3) = 7.5 meters
Step 2: Find the position of the object at 0 seconds.
Plug in t = 0 into the equation s(t) = (2t^2 - t) / (t - 1):
s(0) = (2(0)^2 - 0) / (0 - 1)
s(0) = 0 / (-1)
s(0) = 0 meters
Step 3: Calculate the average rate of change.
The average rate of change is the difference in position divided by the difference in time:
Average rate of change = (s(3) - s(0)) / (3 - 0)
Average rate of change = (7.5 - 0) / 3
Average rate of change = 7.5 / 3
Average rate of change = 2.5 meters/second
Therefore, the average rate of change of the object after 3 seconds is 2.5 m/s. None of the given answer choices match, so we cannot pick any of them.
To determine the average rate of change of the object after 3 seconds, you need to find the difference in the object's position between t = 3 seconds and t = 0 seconds, and then divide it by the difference in time. Here's how you can calculate it:
1. Substitute t = 3 into the position function s(t) = 2t^2 - t/t - 1:
s(3) = 2(3)^2 - 3/3 - 1
s(3) = 18/2 - 3/2
s(3) = 15/2
2. Substitute t = 0 into the position function:
s(0) = 2(0)^2 - 0/0 - 1
s(0) = 0 - 0/-1
s(0) = 0
3. Calculate the difference in position between t = 3 and t = 0:
ΔS = s(3) - s(0)
ΔS = 15/2 - 0
ΔS = 15/2
4. Calculate the difference in time:
Δt = 3 - 0
Δt = 3
5. Calculate the average rate of change (velocity) by dividing the difference in position by the difference in time:
Average velocity = ΔS/Δt
Average velocity = (15/2) / 3
Average velocity = 15/2 * 1/3
Average velocity = 15/6
Average velocity = 5/2 = 2.5 m/s
Therefore, the average rate of change of the object after 3 seconds is 2.5 m/s. None of the options provided match this result, so none of the given options are correct.