To solve the equation \( V^2 = U^2 + 2as \) for \( U \), follow these steps:

### Step 1: Isolate the \( U^2 \) term
Subtract \( 2as \) from both sides of the equation:

\[
U^2 = V^2 - 2as
\]

### Step 2: Solve for \( U \)
Take the square root of both sides to solve for \( U \):

\[
U = \sqrt{V^2 - 2as}
\]

### Important Note:
- The square root gives both a positive and a negative solution:
  \[
  U = \pm \sqrt{V^2 - 2as}
  \]
- Typically, the positive root is used when \( U \) represents a physical velocity, unless the context of the problem specifies otherwise.

Would you like to see an example problem using this formula?

Here are 5 related questions that might interest you:

1. How do you interpret the negative solution when solving for \( U \)?
2. Can this equation be used if the acceleration \( a \) is negative?
3. How do you solve for \( U \) if you only have the final velocity \( V \) and the acceleration \( a \) but not the displacement \( s \)?
4. How does the displacement \( s \) affect the value of \( U \)?
5. What physical scenarios might lead to the use of this equation?

**Tip:** Always check the discriminant \( (V^2 - 2as) \) before taking the square root, as it must be non-negative for real values of \( U \).

Learn how to solve the equation V^2 = U^2 + 2as for U step-by-step. This problem involves algebraic manipulation, quadratic equations, and square roots. Suitable for advanced high school students.

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