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Homework Help: Confirm correctness of simple newton's second law-type problem?

  1. Feb 26, 2010 #1
    1. The problem statement, all variables and given/known data
    at t=0, a 4kg mass is moving at 2 m/s[tex]\hat{i}[/tex] + 3m/s[tex]\hat{j}[/tex]
    at t=0, F1 and F2 act upon the object
    F1= [1 N + (1/2 N/s)t ][tex]\hat{i}[/tex]
    F2= -(1/3 N/s2)t2 [tex]\hat{j}[/tex]

    a) what is the object's velocity when t=3?
    b) at what time does the object stop moving in [tex]\hat{j}[/tex] direction?
    c) what is the object's displacement when t=6?

    2. Relevant equations

    3. The attempt at a solution
    just look at the steps and see if i'm doing it right please

    [tex]\vec{V}[/tex]0 = 2 m/s[tex]\hat{i}[/tex] + 3m/s[tex]\hat{j}[/tex]
    [tex]\vec{F}[/tex](t) = [1 N + (1/2 N/s)t ][tex]\hat{i}[/tex] - (1/3 N/s2)t2 [tex]\hat{j}[/tex]

    [tex]\vec{F}[/tex](t) = m[tex]\vec{a}[/tex]
    [tex]\vec{F}[/tex](3)/4 kg = [tex]\vec{a}[/tex]

    Use [tex]\vec{V}[/tex]f = [tex]\vec{V}[/tex]0 + [tex]\vec{a}[/tex]t

    [tex]\vec{V}[/tex]f = 21/8 [tex]\hat{i}[/tex] - 3/4 [tex]\hat{j}[/tex]

    just look at the [tex]\hat{j}[/tex] component of the vector

    [tex]\vec{F}[/tex]j(t)/ 4kg = [tex]\vec{a}[/tex]j
    Use [tex]\vec{V}[/tex]f = [tex]\vec{V}[/tex]0 + [tex]\vec{a}[/tex]t

    0 = 3m/s[tex]\hat{j}[/tex] - [tex]\vec{a}[/tex]jt

    t = 3.30 s

    [tex]\vec{F}[/tex](t)/ 4kg = [tex]\vec{a}[/tex](t)

    actually, now when i'm rewriting it, i'm not sure how to integrate [tex]\vec{a}[/tex]

    do i integrate the acceleration from 0 to 6? i don't think so...

    i integrated acceleration (not accounting for C) and then integrated velocity from 0 to 6 (this is obviously wrong now that i'm looking over it)
  2. jcsd
  3. Feb 26, 2010 #2


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    Homework Helper

    Find the velocity and acceleration along i and j directions separately.
    Using proper kinematic equations find the remaining answers by using vector addition.
  4. Feb 27, 2010 #3

    which part are you talking about?
  5. Feb 27, 2010 #4


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    Homework Helper

    Voi = 2 m/s, F1i = 1N. Find a1i.
    Similarly find Voj, F2j and a2J.
    Calculate Vfi and Vfj after 3 s.
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