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 of a body -calc

  1. Sep 1, 2006 #1
    The motion of a body is given by the equation dV(t)/dt = 0.6 - 3V(t)
    where V(t) is the speed (in m/s) at time t (in second). If the body was at rest at t = 0

    1) What is the magnitude of the inital acceleration?
    2) The speed of the body varies with time as

    (A) [tex](1 - e^-^3^t) [/tex]
    (B) [tex]2(1 - e^-^3^t)[/tex]
    (C) [tex]\frac{2}{3}(1 - e^\frac{-3t}{2})[/tex]
    (D) [tex]\frac{2}{3}(1 - e^\frac{-3t}{3})[/tex]

    (B) is the correct answer for Q(2) . But how do you arrive at it? And how did they manage to get a 'e' in the answer?

    Please help.
    Last edited: Sep 1, 2006
  2. jcsd
  3. Sep 2, 2006 #2


    User Avatar
    Homework Helper

    Please show what you've tried.

    You're dealing with a separable differential equation, do you know how to solve one?
  4. Sep 2, 2006 #3
    what is a separable equation? I know basic calculus. but i have no clue on how to arrive at the answer to this question,
  5. Sep 2, 2006 #4


    User Avatar
    Homework Helper

    I googled for "separable differential equation" and found a decent looking text:

    Applying the above to your problem:

    [tex]\frac{dV(t)}{dt} = 0.6 - 3V(t)[/tex]

    [tex]dV(t) = (0.6 - 3V(t))dt[/tex]

    [tex]\frac{dV(t)}{0.6 - 3V(t)} = dt[/tex]

    [tex]\int_{V_0}^{V}\frac{dV(t)}{0.6 - 3V(t)} = \int_{t_0}^t dt[/tex]

    (You could also use indefinite integral, and solve for the C with the information given in the problem ie. "body was at rest at t = 0")

    Can you manage the rest?

    PS. There's something wrong with the equation or the correct answer. With the given equation you should arrive at:

    To get the given answer (B), the original equation should be:
    [tex]\frac{dV(t)}{dt} = 6 - 3V(t)[/tex]
    Last edited by a moderator: Apr 22, 2017
  6. Sep 2, 2006 #5


    User Avatar
    Science Advisor

    If you do not know how to solve differential equations, and presumbably aren't expected to here, sSince you are given 4 possible functions, work the other way. Plug each into the equation of motion and see which works. ([itex]\frac{dV}{dt}= 0.6- 3V[/itex] won't work with any of them- as said, it must be 6- 3V.)

    As for part A, that's easy. Just evaluate [itex]\frac{dV}{dt}= 0.6- 3V[/itex] at t= 0. (Of course, you are told V(0).)
  7. Sep 2, 2006 #6
    I am not very sure on how to procede from here.(I have just started learning calculus last week). Anyway should I use
    [tex] \int uv =u \int v - \int \frac{(du)}{(dx)}\int v [/tex] rule?
    Last edited: Sep 2, 2006
  8. Sep 2, 2006 #7


    User Avatar
    Homework Helper

    Here's a formula that should help you:

    [tex]\int \frac{dx}{x} = \ln |x| + C[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook