Solving two simultaneous Equations

Finding Magnitude of two vectors:

An identity (very basic)

Solving Quadratic Equation

There are three ways to solve quadratic equations:

i-                    Factorization

ii-                   Completing Square

iii-                 Using formula

Factorization:

                If you can compute factors easily then this method is the best and the fastest. Here is an example:

Finding factors is a hit and trial method but practice makes things easy.

Cutting short the process, here are the factors:

The values of x are:

Completing Square:

                We know that:

                In this method our major goal is to achieve the above axiom, for example,

Quadratic Formula:

                For equation:

An exponential question

Equations of Motion

There are four basic equations of motion related to linear projection of an object.
There are a few terms that should be known before using these equations:

Time:                 t
Distance:           s
Velocity: Rate of change of distance, 

              Initial velocity = u
              Final velocity = v
Acceleration: Rate of change of velocity,

EQUATIONS OF MOTION:
i - Finding final velocity, given intial velocity, acceleration and time:

ii - Finding final velocity, given initial velocity, acceleration and distance:

iii - Finding distance given average velocity and time:

iv - Finding distance given initial velocity, time, and acceleration:

Special Case:
To find the distance given only velocities and acceleration, rearrange the equation no.2 as shown,

If the problem is related to free fall, initial velocity can be zero.