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     Velocity is defined as change of displacement per unit  time.  Usually velocity is measured with respect to an inertial frame of reference, ie., a coordinate system which does not move.  So we choose the distant star in the universe which is stationary as the reference, and measure all velocities wrt to it.

   In our world we measure velocities wrt objects that are stationary on Earth.  So velocity is measured as a relative quantity.

Acceleration is defined as change of velocity per unit time.  That is
          a = (v - u) / Δt

let  v and u  be measured relative to a frame of velocity    v₀.   Then the absolute velocities of an object at two points of time are:  v + v₀  and  u  + v₀  respectively.

     Then acceleration a = [v + v₀  - u - v₀ ] / Δt
                     a = (v - u) / Δt

Thus acceleration is absolute, whether we take absolute velocities or relative velocities of a particle to compute it.

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What if acceleration is measured with respect to an non-inertial frame of reference? Will the acceleration remain absolute then?
In that case. the accelerating frame of reference will be specified explicitly. An accelerating frame of reference means, that there are forces, pseudo forces etc. The above statement was made for frame of reference which is stationary or moving with a uniform velocity. and, there are no pseudo forces acting..