Results 1 to 2 of 2

Math Help - Maximum Difference

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    1

    Exclamation Maximum Difference

    I have a problem that I am working on called "Calvin and Phoebe's Velocity Problem."

    The two characters distance equations are given as:
    Calvin: s(t)=t^3
    Phoebe: s(t)=e^(t) - 1
    s is feet and t is seconds.

    Part one was to decided which one had the greatest initial acceleration. I figured it was Phoebe by entering 1 into each equation
    Phoebe: 1.71828
    Calvin: 1

    Next was to find when Calvin catches up with phoebe. This was there I had problems. I was not able to do this algebraically, but finding the intersection graphically I got t=1.545. But I need to know how to do it algebraically.

    I also have to find the maximum distance between the two cars on the interval (1,1.545). I started by setting D=(e^(t) - 1) - (t^3)
    I thought I had to then take the derivatives and set that equal to zero, then solve for t, but when I did that i get stuck when i reach t=ln(3t^2). Where would I need to go from there? Solving graphically I got .91 ft

    I also have to find maximum difference in velocity, which I am guessing is done similarly to the one previously. Again I get stuck when setting the derivatives equal to 0. Graphically I got .2157 ft/sec.

    It would be greatly appreciated if anybody could help me with what I am doing wrong, how to find these answers algebraically. Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,888
    Thanks
    682
    Quote Originally Posted by TheEdge View Post
    I have a problem that I am working on called "Calvin and Phoebe's Velocity Problem."

    The two characters distance equations are given as:
    Calvin: s(t)=t^3
    Phoebe: s(t)=e^(t) - 1
    s is feet and t is seconds.

    Part one was to decided which one had the greatest initial acceleration. I figured it was Phoebe by entering 1 into each equation
    Phoebe: 1.71828
    Calvin: 1

    Next was to find when Calvin catches up with phoebe. This was there I had problems. I was not able to do this algebraically, but finding the intersection graphically I got t=1.545. But I need to know how to do it algebraically.

    I also have to find the maximum distance between the two cars on the interval (1,1.545). I started by setting D=(e^(t) - 1) - (t^3)
    I thought I had to then take the derivatives and set that equal to zero, then solve for t, but when I did that i get stuck when i reach t=ln(3t^2). Where would I need to go from there? Solving graphically I got .91 ft

    I also have to find maximum difference in velocity, which I am guessing is done similarly to the one previously. Again I get stuck when setting the derivatives equal to 0. Graphically I got .2157 ft/sec.

    It would be greatly appreciated if anybody could help me with what I am doing wrong, how to find these answers algebraically. Thank you.
    you got part one correct, but your method is wrong.

    initial acceleration is measured at time t = 0

    for calvin ...
    s(t) = t^3
    v(t) = 3t^2
    a(t) = 6t

    for phoebe ...
    s(t) = e^t - 1
    v(t) = e^t
    a(t) = e^t

    note that at t = 1, calvin's acceleration is greater ... 6 > e

    at t = 0, phoebe's acceleration is greater ... e^0 = 1 > 6(0) = 0

    part 2 is correct ... calvin catches up at t = 1.545
    you cannot solve this equation using methods of elementary algebra.


    distance between the two is the absolute value of the difference in their position functions ...

    D = |t^3 - (e^t - 1)|

    graph this on the given interval to find the max difference.


    difference in velocity, V = |3t^2 - e^t|


    once again, note that this is strictly a calculator driven problem ... you will not be able to solve these equations algebraically.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. What's the difference? Need Help!
    Posted in the Calculus Forum
    Replies: 23
    Last Post: June 8th 2014, 08:12 AM
  2. Replies: 3
    Last Post: June 29th 2011, 05:57 PM
  3. Sum and Difference
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 11th 2008, 02:51 PM
  4. difference between finite element/finite difference method
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: October 2nd 2008, 11:03 AM
  5. difference between........
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 7th 2007, 03:18 AM

Search Tags


/mathhelpforum @mathhelpforum