Results 1 to 2 of 2

Thread: Velocity, Integrals, and Riemann Sums

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    5

    Velocity, Integrals, and Riemann Sums

    Table given:


    Rocket A has positive velocity v(t) after being launched upward from an initial height of 0 feet at time $\displaystyle t=0$ seconds. The velocity of the rocket is recorded for selected values of $\displaystyle t$ over the integral $\displaystyle 0 \leq t \leq 80$ seconds, as shown in the table above.

    a. Find the average acceleration of rocket A over the time interval $\displaystyle 0 \leq t \leq 80$ seconds.

    b. Explain the meaning of $\displaystyle \int_{10}^{70} {v(t)dt}$ in terms of the rocket's flight. Use a midpoint Riemann sum with 3 subintervals of equal length to approximate $\displaystyle \int_{10}^{70} {v(t)dt}$.

    c. Rocket B is launched upward with an acceleration of $\displaystyle a(t) = \frac{3}{\sqrt{t+1}}$ feet per second per second. At time $\displaystyle t=0$ seconds, the initial height of the rocket is 0 feet, and the initial velocity is 2 feet per second. Which of the two rockets is traveling faster at time $\displaystyle t=80$ seconds? Explain.

    Thanks a lot to anyone who can help on this!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,002
    Thanks
    1
    One thing you could do to start out is use the given points to find an equation describing the rocket's velocity over time. It is a quadratic.

    I used Excel and got $\displaystyle v(t)=\frac{-1}{200}t^{2}+\frac{19}{20}t+5$

    Acceleration is the derivative of the velocity. Therefore, the integral of velocity is position.

    Average acceleration is

    $\displaystyle \frac{\text{change in velocity}}{\text{time elapsed}}=\frac{v(t_{1})-v(t_{0})}{t_{1}-t_{0}}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with Riemann Sums and Definite Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Jun 7th 2010, 05:24 AM
  2. Replies: 1
    Last Post: Nov 19th 2009, 10:10 PM
  3. Riemann Sums and Integrals
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Aug 29th 2009, 09:04 AM
  4. Riemann Sums
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 16th 2007, 08:12 AM
  5. Riemann Sums and Riemann Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 1st 2006, 01:08 PM

Search Tags


/mathhelpforum @mathhelpforum