Kinematics and calculus

A particle moves with vms^-1 where:

v = 0.16t^3 -0.12t +10.6 (for t is greater than/equal to 0 and t is less than/equal to 5)
v = 40-2t (for t > 5)

Find the two times for when the particle is 200m away from the starting point.

I've solved 0=40-2t to find the greatest possible value for t
I tried to integrate and factorise 40-2t to get two values for t which are apparently incorrect
I'm not sure why the first equation for v is significant in the question

When you integrate the velocity for t>5 to get a quadratic, the constant will be determined by the value of the first part (integrated) when t=5 as the distance must be continuous at t=5.

Im guessing that the first part (integrated) is smalll in magnitude (<200) when t<5