https://file.aiquickdraw.com/mathbot/file/1729775331764g3kzgtzq.jpg

The formula provided in the image is:

\[
S = ut + \frac{1}{2} a t^2
\]

where:
- \( u = 12 \) (initial velocity),
- \( a = 10 \) (acceleration), 
- \( t = 8.5 \) (time).

Let's substitute these values into the formula and calculate \( S \).

### Step-by-step calculation:
\[
S = (12 \times 8.5) + \frac{1}{2} \times 10 \times (8.5)^2
\]

1. \( 12 \times 8.5 = 102 \)
2. \( (8.5)^2 = 72.25 \)
3. \( \frac{1}{2} \times 10 \times 72.25 = 5 \times 72.25 = 361.25 \)
4. \( S = 102 + 361.25 = 463.25 \)

Thus, the value of \( S \) is **463.25 units**.

Would you like further details or have any questions? 

Here are 5 related questions to expand this:
1. How does the formula \( S = ut + \frac{1}{2}at^2 \) relate to real-world motion?
2. How would the result change if \( a \) (acceleration) were negative?
3. What is the physical meaning of each term in the formula?
4. How would you calculate the velocity after 8.5 seconds?
5. How does the formula differ if acceleration is not constant?

**Tip**: Always check your units when dealing with physical formulas to ensure consistency.

Given the formula S = ut + (1/2)at², when u = 12, a = 10, and t = 8.5, find the value of S.

Learn how to solve a kinematics problem using the formula S = ut + (1/2)at². With u = 12, a = 10, and t = 8.5, this step-by-step solution covers key concepts like algebra and motion equations. Suitable for students in Grades 9-12.

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