The third equation of motion, which is v^2 - u^2 = 2as, is the correct answer.

Explanation:

In physics, motion can be described using three equations known as the equations of motion. These equations relate the final velocity (v), initial velocity (u), acceleration (a), and distance or displacement (s) of an object.

The third equation of motion, v^2 - u^2 = 2as, is derived from the other two equations of motion. It is used to calculate the final velocity or initial velocity of an object when the other variables are known.

Let's break down the equation and understand its components:

1. v: Final velocity of the object.
2. u: Initial velocity of the object.
3. a: Acceleration of the object.
4. s: Distance or displacement covered by the object.

Now, let's understand how this equation is derived:

To derive the equation, we start with the first equation of motion: v = u + at.

1. Rearranging the equation: v - u = at.

2. Multiplying both sides of the equation by (v + u): (v - u)(v + u) = at(v + u).

3. Using the identity (a - b)(a + b) = a^2 - b^2, we simplify the equation: v^2 - u^2 = at(v + u).

4. Dividing both sides of the equation by 2: (v^2 - u^2)/2 = at(v + u)/2.

5. Simplifying further: (v^2 - u^2)/2 = as + au.

6. Since v = u + at, we can substitute this value in the equation: (v^2 - u^2)/2 = as + a(u + at).

7. Expanding the equation: (v^2 - u^2)/2 = as + au + a^2t.

8. Simplifying: (v^2 - u^2)/2 = as + a(u + at).

9. Rearranging the equation: v^2 - u^2 = 2as + 2a^2t.

10. Assuming constant acceleration (a^2t is negligible), we get: v^2 - u^2 = 2as.

Thus, we have derived the third equation of motion: v^2 - u^2 = 2as.

This equation is particularly useful when we need to find the final velocity of an object or the initial velocity when the other variables are known. It relates the change in velocity (v^2 - u^2) to the acceleration (a) and displacement (s) of the object.

That is the third equation of motion. it is called position velocity relation