Mechanics

v = 2 for 0 < t <= 10
So for t = 10, s = 20

for t > 10, v= 0.03*t^2 - 0.3*t + 2

"Show that for: t > 10, s = 0.01*t^3 - 0.15*t^2 + 2t + 5"

Why is it '+ 5' at the end and not '+ 20'?

By integration, s = 0.01*t^3 - 0.15*t^2 + 2t + c

Substitute s = 20, t = 10 :

20 = 10 - 15 + 20 + c
c = 5