The problem provides a formula relating the final velocity ($v$) of an object to its initial velocity ($u$), acceleration ($a$), and distance ($s$): $v^2 = u^2 + 2as$. We are given the initial velocity $u = 30$ m/s, the acceleration $a = 5$ m/s$^2$, and the distance $s = 320$ m. We need to calculate the final velocity $v$.

1. Problem Description

The problem provides a formula relating the final velocity ($v$) of an object to its initial velocity ($u$), acceleration ($a$), and distance ($s$): $v^2 = u^2 + 2as$. We are given the initial velocity $u = 30$ m/s, the acceleration $a = 5$ m/s$^2$, and the distance $s = 320$ m. We need to calculate the final velocity $v$.

2. Solution Steps

First, we write down the given formula:

$v^2 = u^2 + 2as$

Next, we substitute the given values into the formula:

$v^2 = (30)^2 + 2(5)(320)$

$v^2 = 900 + 10(320)$

$v^2 = 900 + 3200$

$v^2 = 4100$

Now, we take the square root of both sides to solve for $v$:

$v = \sqrt{4100}$

$v = \sqrt{100 \times 41}$

$v = 10\sqrt{41}$

$v \approx 64.03$ m/s

3. Final Answer

The final velocity is approximately 64.03 m/s.