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Integrals and Acceleration.

  1. Jul 28, 2008 #1
    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?

    I'm using the rules of integrals
    No idea where to start.
  2. jcsd
  3. Jul 28, 2008 #2
    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)
  4. Jul 28, 2008 #3


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    Staff Emeritus
    Science Advisor

    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?
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