Relation between Acceleration, Velocity and Displacement

The phase relation as well as the magnitudes of acceleration, velocity and displacement become evident when we make the integral or time derivative respectively (thanks to Sir Isaac Newton)

​​​With the acceleration a as reference

the velocity v is the integral of a

 

​and the displacement d becomes

 

 

 

With reference to the displacement

 

the velocity is the fist time derivative

and the acceleration becomes