1st Equation of Motion:

The first equation of motion relates the final velocity (v), initial velocity (u), acceleration (a), and displacement (s) of an object. It is given by the equation:

v = u + at

Where:
- v is the final velocity of the object
- u is the initial velocity of the object
- a is the acceleration acting on the object
- t is the time taken

Explanation:
- The first equation of motion is derived by considering a constant acceleration scenario.
- Initially, let's assume the object starts from rest, so the initial velocity (u) is zero.
- The average velocity of the object can be calculated by dividing the final velocity by 2, as the acceleration is constant.
- The average velocity is given by (v + u) / 2.
- The displacement (s) can be calculated by multiplying the average velocity by the time taken (t).
- Since the average velocity is (v + u) / 2, we can substitute it in the displacement equation to get s = ((v + u) / 2) * t.
- Simplifying this equation, we get 2s = (v + u) * t.
- Rearranging the equation, we obtain v = u + at, which is the first equation of motion.

2nd Equation of Motion:

The second equation of motion relates the final velocity (v), initial velocity (u), acceleration (a), and displacement (s) of an object. It is given by the equation:

v^2 = u^2 + 2as

Where:
- v is the final velocity of the object
- u is the initial velocity of the object
- a is the acceleration acting on the object
- s is the displacement covered by the object

Explanation:
- The second equation of motion is derived using the first equation of motion and the formula for average velocity.
- We know from the first equation of motion that v = u + at.
- By rearranging this equation, we get t = (v - u) / a.
- Substituting this value of t in the formula for displacement (s = ((v + u) / 2) * t), we get s = ((v + u) / 2) * ((v - u) / a).
- Simplifying this equation, we get s = (v^2 - u^2) / (2a).
- Rearranging the equation, we obtain v^2 = u^2 + 2as, which is the second equation of motion.

3rd Equation of Motion:

The third equation of motion relates the final velocity (v), initial velocity (u), acceleration (a), and displacement (s) of an object. It is given by the equation:

s = ut + (1/2)at^2

Where:
- s is the displacement covered by the object
- u is the initial velocity of the object
- t is the time taken
- a is the acceleration acting on the object

Explanation:
- The third equation of motion is derived by eliminating the final velocity (v) from the first and second equations of motion.
- From the first equation of motion, we have v = u + at.
- Squaring both sides of the equation, we get v^2 = u^2 + 2aut + a^2t^2.
- Rearr