Integrated Math III - Problem Set 5 by Evan Jenkins

# 1

ccheungalmodovar1 — 2025-07-10 21:36:14 UTC

# 2

ccheungalmodovar1 — 2025-07-10 21:46:11 UTC

Question 1

hchau7 — 2025-07-10 21:46:37 UTC

Question 3

hchau7 — 2025-07-10 21:47:12 UTC

Part 1

echapman89 — 2025-07-14 19:43:14 UTC

Using both methods (split the difference and equidistant) to determine the value of s prime at a give t. We saw a pattern continue to create our equation for velocity/ s prime.

Part 2

echapman89 — 2025-07-14 19:44:28 UTC

Part 2 graph'd

echapman89 — 2025-07-14 19:45:32 UTC

Part 3

echapman89 — 2025-07-14 19:46:45 UTC

Although S has a constant (c), the equation for s prime does not.

Part 4: S = at^2 + c

echapman89 — 2025-07-14 19:47:57 UTC

#3

ccheungalmodovar1 — 2025-07-14 19:53:05 UTC

What would s’ be if the formula for a moving object were s=2t2?

bpepe10 — 2025-07-14 20:06:09 UTC

The table shows a second difference of 4. I used the average rate of change for the 2 second interval 3 to 5 as 16. Then, I also found the average rate of change for the one second intervals 3 to 4 and 4 to 5, which were 14 and 18 respectively. The average of those intervals ((14+18)/2) also equals 16. If I then use the number that is the second difference (4) and multiply it by 4 seconds, I will again get an s' value of 16. Therefore, the formula for s'=4t

Problem 3- What is s' if s=4t^2+7?

ssewpersaud2 — 2025-07-14 20:07:15 UTC

We found the common second difference of 8, by this point we realized s' was just the common second difference times t. We thought that the +7 at the end of the equation didn't change the outcome of our s' equation because the 7 changed the starting point and not the actual velocity. s'=8t

#4

cflores324 — 2025-07-14 20:09:37 UTC

The second difference is 8.

S' at t= 3 is 24.

We noticed the coefficient 4 multiplied the coefficient, 2 is 8. And...8*3 is 24 which matches our S' calculation for t=3.

We believe that in general, given s=at^2+c, s' = 2at. We believe c affects position but not velocity.

Problem 2

agonzalez2_175 — 2025-07-14 20:09:52 UTC

We got a second difference of 6. Therefore, s'=6t

Extension 5

bpepe10 — 2025-07-14 20:13:18 UTC

Using both the table and the average rate of change...the s' formula for at2+bt+c would be 2at+b. The c value (the constant) effects starting position, but does not effect velocity.

Question 4

hchau7 — 2025-07-14 20:22:40 UTC

#4 part 1

ccheungalmodovar1 — 2025-07-14 20:30:58 UTC

# 4 part 2

ccheungalmodovar1 — 2025-07-14 20:31:28 UTC

Extension 6

rashley12 — 2025-07-14 20:48:39 UTC

Unclear yet on a formula for s'. Using the strategy of "splitting the difference" gives the velocity at any point.

cveigl1 — 2025-07-16 19:38:43 UTC

cveigl1 — 2025-07-16 19:39:00 UTC

cveigl1 — 2025-07-16 19:39:12 UTC

ewiggins26 — 2025-07-16 19:43:37 UTC