Understanding Motion: Solving Problems with Integrals and Acceleration

[myanmar]

I'm doing some stuff with integrals, and my homework has these problems. I'm quite confused. Any help would be nice, although I don't want you to solve them for me. I know my integrals (I did problems 1-8 fine, which was just taking integrals), but have no idea how to do this.

9. Find the position function s(t) given acceleration a(t) = 3t if v(2) = 0
and s(2) = 1.
10. An object in rectilinear motion has acceleration a(t) = 12t - 6. If the
velocity at time t = 2 is -3, and the position at time t = 1 is 4, nd
the position function, s(t), for the object.
11. A particle starts moving along the x-axis from the point (100, 0),
(distance in meters) and with an initial velocity of 25 m/min. If the
acceleration is given by the equation a(t) = 13sqrt(t), what is the equation
of motion of the particle?
The next two questions involve the following situation: An
astronaut stands on a platform 3 meters above the moon's surface and
throws a rock directly upward with an initial velocity of 32 m/s.
12. Given that the acceleration due to gravity on the moon's surface is 1.6
m/sec^2, derive an equation which gives the height of the rock at time
t seconds (valid while the rock is in the air).
13. How high will the rock travel?
14. A bocce ball is accidentally dropped from a building 98m high. How
long does it take for the bocce ball to hit the gound, given that the
acceleration due to gravity is 9.8 meters per second per second?
The next two questions involve the following situation: A
particle moving along the number line has acceleration given by a(t) =
2t - 1. We also know that s0 = 2 and v0 = -2.
15. What is the net distance traversed from time t = 0 to t = 3?
16. What is the total distance traversed from time t = 0 to t = 3?

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I'm using the rules of integrals
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No idea where to start.

 

[cryptoguy]

Questions 9/10/11. If you know acceleration, can you find a function for velocity? And if you know the function for velocity, can you find a function for displacement?
Keep in mind C (constants)

 

[HallsofIvy]

Perhaps you need to think the other way: If you are given a position function, how do you find the velocity function? The acceleration function? How do you reverse those?