# Urgent ------> Q. definition of displacement and distinguish between uniformly and non uniformly accelerated motion

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2015-06-20T14:36:11+05:30

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Displacement 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 constants
Summary = 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.