is the shortest distance between the initial and final position of a body. It is a vector quantity, meaning it has a direction associated with it.Uniformly accelerated motion
: The acceleration is constant which means that equal increments in velocity in equal interval of time.
Hence v = at + c, where c is some constant depending upon the initial velocity of the body and t is the time
The displacement is given by:
, where c1 and c2 are constantsSummary = Velocity profile is linear and displacement profile is parabolic.Non-uniformly accelerated motion
: The acceleration is variable which means that acceleration itself is a function of time
, a(t) denotes acceleration as a function of time
Hence v =
The displacement is given by:Summary = Velocity profile is at least parabolic and displacement profile is at least cubic.
Velocity and displacement profiles are based on the assumption that acceleration is a polynomial function of time.