A particle 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

Answer:

the position of the particle is:

s (t) = (1.5 / 2) t ^ 2 - 28.75