Indefinite Integrals

A hoist mechanism raises a crate with an acceleration (in m/s^2)
a=√1+0.2t , where t is time in seconds. Find the displacement of the crate as a function of time if v=0m/s and s=2m fot t=0s.

v(t)=integral of a= 1/0.2 *(1+0.2t)^(3/2)*(2/3)+C=10/3*(1+0.2t)^(3…
v(0)=0
10/3+C=0
C=-10/3

v(t)=10/3*(1+0.2t)^(3/2)-10/3
s(t)= integral of v(t)= 5*10/3*(1+0.2t)^(5/2)*(2/5)-10/3t+c
s(t)=20/3(1+0.2t)^(5/2)-10/3t+c
s(0)=2
20/3(1+0.2(0))^(5/2)-10/3(0)+c=2
c=-14/3

s(t)=20/3(1+0.2t)^(5/2)-10/3t-14/3