An object at the origin at time t= 0 has velocity measured in meters per second,

Question

v(t) = t/30 if 0 <= t <= 90
= 3 if 90 < t <= 108
= 9-(t/30) if 180 < t

When, if ever, does the object return to the origin? t=

Answer 1

s(t)
= t^2/15 if 0 <= t <= 90
= 90^2/15 + 3(t-90) if 90 < t <= 108
= 594 + 9(t-108) - (t-108)^2/15 if 180 < t

s(t) = 0 when t=291.54