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 Answer: the position of the particle is: s (t) = (1.5 / 2) t ^ 2 - 28.75
