An automobile accelerates from rest at 1+ 3* sqrt (t) mph/sec for 9 seconds.
how far does it travel in those 9 sec?

Writing the acceleration as a function of time:
a(t) = 1 + 3√t

Integrating acceleration, we obtain velocity:
v(t) = t + 2(t)^(3/2) + c;
object at rest so velocity at t = 0 is 0 so c = 0.
v(t) = t + 2(t)^(3/2)

Integrating velocity to obtain an equation for displacement:
d(t) = t²/2 + 4/5 t^(5/2) + c
Applying limits from t = 0 to t = 9
d = 9²/2 + 4/5 9^(5/2)
d = 234.9 m

Sounds propagates through some kind of medium. usually it's air, but it goes just as well through solid objects like walls, windows etc. a soundwave will compress the (air)molecules in front of it, and if this increased density wave hits your ears, you register it as sound. solid objects like walls are a lot denser than air, this means that they will damp a wave, but also carry it easier.

The waves slow downn