# Velocity Calculator v^2 = u^2 + 2as

## Calculator Use

This velocity calculator uses the equation that the final velocity of an object is equal to its initial velocity added to its acceleration multiplied by time of travel. This calculator does assume constant acceleration during the time traveled. This calculator can be used to find initial velocity, final velocity, acceleration or time as long as three of the variables are known.

## Velocity Equations for these calculations:

Final velocity (v) squared equals initial velocity (u) squared plus two times acceleration (a) times displacement (s).

Solving for v, final velocity (v) equals the square root of initial velocity (u) squared plus two times acceleration (a) times displacement (s).

Where:

v = final velocity

u = initial velocity

a = acceleration

s = displacement

Use standard gravity, a = 9.80665 m/s^{2}, for equations involving the Earth's gravitational force as the acceleration rate of an object.

## Velocity equation solved for different variables and used in this calculator:

Solving for the different variables we can use the following formulas:

- Given u, a and s solve for v

Given initial velocity, acceleration and displacement, solve for the final velocity.- \( v = \sqrt{ u^2 + 2as } \)

- Given v, a and s solve for u

Given final velocity, acceleration and displacement, solve for the initial velocity.- \( u = \sqrt{ v^2 - 2as } \)

- Given v, u and s solve for a

Given final velocity, initial velocity and displacement, solve for the acceleration.- \( a = \dfrac{ v^2 - u^2 }{2s} \)

- Given v, u and a solve for s

Given final velocity, initial velocity and acceleration, solve for the displacement.- \( s = \dfrac{ v^2 - u^2 }{2a} \)