1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Motion Question (Dynamics)

  1. Oct 21, 2007 #1
    [SOLVED] Motion Question (Dynamics)

    EDIT: I just realised this question was better suited in this forum than the engineering one, sorry :(

    1. The problem statement, all variables and given/known data

    The rocket sled starts from rest and accelerates at a = 30 + 2t until its velocity is 400m/s. It then hits a water brake and its acceleration is a = -0.003v^2 m/s^2 until its velocity decreases to 100 m/s. What total distance does it travel?

    2. Relevant equations

    v = u + at
    s = ut + at^2/2
    v^2 = u^2 + 2as

    3. The attempt at a solution

    I'm pretty sure my first part is correct but here it is anyway:

    v = u + at
    v = u + (30 + 2t)t
    *Sub in values and i get t = 8.508s, then i get s = 1701.652m from the other equation

    For the next part ive done this:

    a = -0.003v^2
    v dv/dx = -0.003v^2
    dv/v = -0.003dx *integrate both sides

    ln(v) = -0.003x + C

    when v = 400, x = 0, C = ln(400)

    ln(v) = -0.003x + ln(400)

    so when v = 100, i get x = 462.098m

    So the total distance i get is 2163.750m but the answer says 2300m....

    Where did i go wrong or is the answer given incorrect? :S
  2. jcsd
  3. Oct 21, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    The equations you give only hold for constant acceleration. The acceleration function you give (a=30+2t) is not constant, and so you will need to use calculus to solve even the first part.
  4. Oct 21, 2007 #3
    Ahh whoops, i see it now :)

    Now i get the first part with t = 10s and a displacement of 1833.333m

    Thanks cristo!
  5. Oct 21, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    You're welcome!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook