v = 5t²+2t

vdt = (5t²+2t)dt

Integrating,

vt = 5t³/3 + t² + c

vt = S,

S = 5t³/3 + t² + c,

When time is zero, displacement is zero.

Therefore, 0 = 0 + 0 + c

c=0

S = 5t³/3 + t²

Put t = 2,

S = 40/3 + 4 = 52/3

Put t=1,

S= 5 /3+ 1 = 8/3

Therefore, the distance travelled in the 2nd second = 52/3-8/3 = 44/3