V (t) = t^2+2 (m/s)

For t=0, x (0) = 4m

Find the acceleration and the kinematic equation

Acceleration can be found by differentiating v (t) by t:

dv/dt = d (t^2+2) / dt

=d (t^2) / dt + d (2) / dt

=2tdt/dt + 0

=2t

The displacement x (t) can be found by integrating v (t) by t

x (t) = int (t^2 + 2) dt

= t^3/3 + 2t + c

When t=0, x (0) = 4=0+0+c

So c=4

x (t) = t^3/3 + 2t + 4

v (t) = t^2 + 2

a (t) = 2t