Second Equation Of Motion Formula

The second equation of motion, also known as the equation of final velocity, can be derived from the first equation of motion. It is given as:

v² = u² + 2as

Where:

• v is the final velocity
• u is the initial velocity
• a is the acceleration
• s is the displacement

This equation is used when the time of motion is not known. It relates the final velocity and displacement of a moving object to its initial velocity and acceleration.

Here's a step-by-step derivation of the second equation of motion:

1. Start with the first equation of motion: v = u + at
2. Multiply both sides by t: vt = ut + at²
3. Rearrange the equation to get: at² = vt - ut
4. Now, multiply the equation by 2a: 2as = 2avt - 2aut
5. We know that 2avt = v² (from the first equation of motion, v = u + at, multiply both sides by v)
6. Substitute 2avt with v² in the equation: 2as = v² - 2aut
7. Rearrange the equation to get the second equation of motion: v² = u² + 2as