Direction: The table gives the position​ s(t) of an object moving along a line at time​ t, over a​ two-second interval. Find the average velocity of the object over the following intervals.

a.​ [0, 2]
b.​ [0, 1.5]
c.​ [0, 1]
d.​ [0, 0.5]

t= 0, 0.5, 1, 1.5, 2
s(t)= 0, 22, 48, 66, 76

^Those numbers were in a table going horizontally and the numbers should align upright. I do not understand how you would set this up. It's asking for the average velocity over these intervals above, A,B,C,D

distance / time

for example from time 0 to 1.5
(66-0) / (1.5-0) = 44

Well, well, it seems we have a math problem here! Average velocity, huh? Don't worry, I'll do my best to assist you.

To find the average velocity, we need to calculate the change in position over the given time interval. So, let's get cracking!

a. [0, 2]
To find the average velocity for this interval, we need to calculate the change in position (s) divided by the change in time (t).
s(2) - s(0) = 76 - 0 = 76
t(2) - t(0) = 2 - 0 = 2
Average velocity = (76 - 0) / (2 - 0) = 76 / 2 = 38 units per second

b. [0, 1.5]
s(1.5) - s(0) = 66 - 0 = 66
t(1.5) - t(0) = 1.5 - 0 = 1.5
Average velocity = (66 - 0) / (1.5 - 0) = 66 / 1.5 ≈ 44 units per second

c. [0, 1]
s(1) - s(0) = 48 - 0 = 48
t(1) - t(0) = 1 - 0 = 1
Average velocity = (48 - 0) / (1 - 0) = 48 / 1 = 48 units per second

d. [0, 0.5]
s(0.5) - s(0) = 22 - 0 = 22
t(0.5) - t(0) = 0.5 - 0 = 0.5
Average velocity = (22 - 0) / (0.5 - 0) = 22 / 0.5 = 44 units per second

And there you have it! The average velocities for intervals A, B, C, and D are 38 units/sec, 44 units/sec, 48 units/sec, and 44 units/sec, respectively. I hope that helps! If not, well, it's an average answer... I tried my best!

To find the average velocity over each of the given intervals, we need to calculate the change in position and divide it by the change in time.

a. Interval [0, 2]:
The change in position (Δs) is s(2) - s(0) = 76 - 0 = 76, and the change in time (Δt) is 2 - 0 = 2. Therefore, the average velocity is Δs/Δt = 76/2 = 38 units per second.

b. Interval [0, 1.5]:
The change in position is s(1.5) - s(0) = 66 - 0 = 66, and the change in time is 1.5 - 0 = 1.5. So the average velocity is 66/1.5 = 44 units per second.

c. Interval [0, 1]:
The change in position is s(1) - s(0) = 48 - 0 = 48, and the change in time is 1 - 0 = 1. Therefore, the average velocity is 48/1 = 48 units per second.

d. Interval [0, 0.5]:
The change in position is s(0.5) - s(0) = 22 - 0 = 22, and the change in time is 0.5 - 0 = 0.5. So the average velocity is 22/0.5 = 44 units per second.

Therefore, the average velocities are:
a. 38 units per second
b. 44 units per second
c. 48 units per second
d. 44 units per second

To find the average velocity of an object over a given time interval, you need to calculate the change in position divided by the change in time.

Let's calculate the average velocity for each interval:

a. [0, 2]
To find the change in position, subtract the initial position from the final position:
Change in position = s(2) - s(0) = 76 - 0 = 76

The change in time is simply the time interval:
Change in time = 2 - 0 = 2

Now divide the change in position by the change in time:
Average velocity = Change in position / Change in time = 76 / 2 = 38

So, the average velocity over the interval [0, 2] is 38.

b. [0, 1.5]
Calculate the change in position:
Change in position = s(1.5) - s(0) = 66 - 0 = 66

The change in time:
Change in time = 1.5 - 0 = 1.5

Average velocity = Change in position / Change in time = 66 / 1.5 = 44

The average velocity over the interval [0, 1.5] is 44.

c. [0, 1]
Change in position = s(1) - s(0) = 48 - 0 = 48

Change in time = 1 - 0 = 1

Average velocity = Change in position / Change in time = 48 / 1 = 48

The average velocity over the interval [0, 1] is 48.

d. [0, 0.5]

Change in position = s(0.5) - s(0) = 22 - 0 = 22

Change in time = 0.5 - 0 = 0.5

Average velocity = Change in position / Change in time = 22 / 0.5 = 44

The average velocity over the interval [0, 0.5] is 44.

So, the average velocities for the given intervals are:
a.​ [0, 2]: 38
b.​ [0, 1.5]: 44
c.​ [0, 1]: 48
d.​ [0, 0.5]: 44