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 $U$.