Aparticle is moving with the given data. find the position of the particle. v(t) = 1.5 t , s(9) = 32

We have the following equation:
 v (t) = 1.5 t
 Rewriting we have:
 s' (t) = 1.5 t
 ds / dt = 1.5 t
 ds = (1.5 t) dt
 Integrating both sides we have:
 s = (1.5 / 2) t ^ 2 + s0
 Looking for the constant we have:
 32 = (1.5 / 2) * (9) ^ 2 + s0
 s0 = 32 - (1.5 / 2) * (9) ^ 2
 s0 = -28.75
 Then, the equation position is:
 s (t) = (1.5 / 2) t ^ 2 - 28.75
 
 the position of the particle is:
 s (t) = (1.5 / 2) t ^ 2 - 28.75