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Motion in 1 Direction

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  1. Sep 25, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle is moving along the x axis. Its velocity as a function of time is given by v = 5+10t , where v is in
    m/s. The position of the particle at t = 0 sec is 20 m. Find
    (a) the acceleration as a function of time
    (b)the position as a function of time
    (c) the velocity of the particle at t = 0 sec.

    2. Relevant equations


    3. The attempt at a solution
    a)
    a=dv(t)/dt=10m/s
    b)
    x(t)=5t +10t^2
    c)
    V(0)= 5+10*(0s)=5m/s
     
  2. jcsd
  3. Sep 25, 2015 #2
    And your question is?
     
  4. Sep 25, 2015 #3

    SteamKing

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    The units of acceleration must be m/s2
    When you integrate a function, you must always include the constant of integration, C.

    Remember, the position of the particle at t = 0 is x(0) = 20 m

    Use this condition to determine C
    This answer is correct
     
  5. Sep 25, 2015 #4
    i am confused if my answer for a) is correct. it asks for acceleration as a function of time, i get 10m/s by computing the derivative of velocity, which does not have t at all
     
  6. Sep 25, 2015 #5
    okay thank you very much. needed confirmation.
     
  7. Sep 25, 2015 #6
    shouldn't b) be x(t)=5t+5t^2+C because V=5+10t, which is the derivative v=dx/dt ?
     
  8. Sep 25, 2015 #7

    SteamKing

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    Velocity always has units of time. Velocity is defined as the time rate of change of position. V(t) will be in units of m/s.

    When you take the time derivative of something, the units of the something get divided by the units of time.

    Also, by definition, an acceleration has units of LT-2, so m/s2 are the correct units.
     
  9. Sep 25, 2015 #8

    SteamKing

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    Yep. You still use the initial position of the particle to determine the value of C.
     
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