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
