This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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.
\frac{dv}{dt} = constant = a
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:
\frac{d^2x}{dt^2} = constant = a\ (assumed)  \\ \frac{dx}{dt} = at+c_1 \\ x = at^2 + c_1t + c_2, 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
 \frac{dv}{dt} = a(t) , a(t) denotes acceleration as a function of time
Hence v =  \int\limits^{t_2}_{t_1} {a(t)} \, dt
The displacement is given by:
\frac{d^2x}{dt^2} = a(t)
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.

1 5 1