Derivation of 2as = v^2 - u^2

To derive the equation 2as = v^2 - u^2, where "a" represents acceleration, "s" represents displacement, "v" represents final velocity, and "u" represents initial velocity, we can start by using the kinematic equations of motion.

Initial Equation:
The initial equation we will use is:
v^2 = u^2 + 2as

Understanding the Variables:
Before proceeding with the derivation, it is important to understand the meaning of each variable in the equation:
- "v" (final velocity) represents the velocity of an object at the end of its motion.
- "u" (initial velocity) represents the velocity of an object at the beginning of its motion.
- "a" (acceleration) represents the rate at which the object's velocity changes.
- "s" (displacement) represents the change in position of the object.

Derivation:
1. Start with the initial equation: v^2 = u^2 + 2as.
2. Rearrange the equation by subtracting u^2 from both sides: v^2 - u^2 = 2as.
3. Divide both sides of the equation by 2: (v^2 - u^2) / 2 = as.
4. Multiply both sides of the equation by 2: 2as = v^2 - u^2.

Conclusion:
By following the steps above, we have derived the equation 2as = v^2 - u^2 from the initial kinematic equation v^2 = u^2 + 2as. This equation relates the final velocity, initial velocity, acceleration, and displacement of an object. It is a useful tool in solving various problems in physics and understanding the motion of objects.