Explanation:

For   0<t<4 s  :

Let the acceleration of the particle be  a  ( constant)

Initial velocity of the particle    u=0

Using       S=ut+21at2                    

∴   x=0+21at2                       ⟹x=2at2          for    0<t<4

Thus the x-t graph is parabola symmetric about x axis   for  0<t<4 

Velocity of particle at t=4 s,       v=0+a(4)=4a  m/s

For   t>4 s  :

Acceleration of the particle is zero   i.e  a=0

∴   x=vt=4at             for  t>4 s

Thus x-t graph is a straight line  for  t>4 s