Given the equation:
[tex]\[ v_f^2 = v_i^2 + 2 a x \][/tex]
we need to solve for [tex]\( x \)[/tex].
Let's proceed step by step:
1. Rewrite the equation:
The given equation is:
[tex]\[ v_f^2 = v_i^2 + 2 a x \][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the equation. Subtract [tex]\( v_i^2 \)[/tex] from both sides:
[tex]\[ v_f^2 - v_i^2 = 2 a x \][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by [tex]\( 2a \)[/tex]:
[tex]\[ x = \frac{v_f^2 - v_i^2}{2 a} \][/tex]
Now plug in the given values:
- [tex]\( v_f = 10 \)[/tex] (final velocity)
- [tex]\( v_i = 2 \)[/tex] (initial velocity)
- [tex]\( a = 3 \)[/tex] (acceleration)
4. Substitute the values into the formula:
[tex]\[ x = \frac{10^2 - 2^2}{2 \cdot 3} \][/tex]
5. Perform the calculations:
[tex]\[ x = \frac{100 - 4}{6} \][/tex]
[tex]\[ x = \frac{96}{6} \][/tex]
[tex]\[ x = 16 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[ x = 16 \][/tex]
