https://file.aiquickdraw.com/mathbot/file/1727436678433bafxsv52.jpg

### Solution:

#### (a) 
To calculate \( s \) when \( a = 0.9 \) and \( t = 4 \):

Using the formula \( s = \frac{1}{2} a t^2 \), we substitute the values of \( a \) and \( t \):
\[
s = \frac{1}{2} \times 0.9 \times (4)^2 = 7.2
\]
Thus, the value of \( s \) is \( 7.2 \).

#### (b)
Rearranging the formula \( s = \frac{1}{2} a t^2 \) to find \( t \) in terms of \( s \) and \( a \):

Solving for \( t \):
\[
t = \sqrt{\frac{2s}{a}}
\]
Or more precisely:
\[
t = -1.414 \cdot \sqrt{\frac{s}{a}}
\]
This represents the negative branch of the square root, but typically, we take the positive value in physics problems.

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Do you want any further details or explanations on this?  
Here are five related questions:
1. How can we handle units in the formula to ensure consistency?
2. Can you explain the physical significance of the constant \( \frac{1}{2} \)?
3. What are the steps to solve for \( t \) algebraically?
4. How would the answer change if \( a \) were negative?
5. Can you calculate \( s \) for different values of \( t \)?

**Tip:** When solving quadratic equations, always consider both positive and negative square root branches unless a physical context specifies otherwise.

Work out the value of s when a = 0.9 and t = 4. Rearrange the formula to find t in terms of s and a.

Learn how to solve for the displacement (s) using the formula s = (1/2) a t^2 when a = 0.9 and t = 4. Additionally, understand how to rearrange the equation to solve for t in terms of s and a. Suitable for students in Grades 9-11.

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