dv/dt = 2t+2

so dv = 2tdt+2dt

on integrating the given eq.

v = t² + 2t + C

at start v = 0 at t = 0

so on puting these initial values we get C = 0 

so v = t² + 2t 

so dx/dt = t² + 2t 

so dx = t²dt + 2tdt 

on integrating x = t³/3 + t²+ C

on putting initial values x=0 at t=0 

we get C = 0

so x =  t³/3 + t² 

now put t = 2