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Homework Help: Change in Momentum using Vectors

  1. Jan 23, 2016 #1
    1. The problem statement, all variables and given/known data
    A force F = (2ti + 3t^2j) N acts on an object moving in the xy plane. Find the magnitude of change in momentum of the object in time interval t=0 to t=2
    (The bold ones are vectors)
    2. Relevant equations
    Ft=change in momentum

    3. The attempt at a solution
    magnitude of F = (4t^2 + 9t^4)^(1/2)
    taking t^2 common:
    Ft=delta p
    so, delta p = 2t(4 + 9t^2 ) ^ (1/2)

    But the answer doesn't have ts in it.
  2. jcsd
  3. Jan 23, 2016 #2
    Have you learnt calculus? The force is time-dependent, so you will have to perform an integration to find out the total change in momentum over the time interval.
  4. Jan 23, 2016 #3
    I have learnt it. But have never actually used it in physics.
    So I integrate F?
    Integration of 2ti+3t^2 j
    is t^2i + t^3j
    with the limits 0 and 2
    4i + 8j is the change in p
  5. Jan 23, 2016 #4
    Yes. You can understand the integration process by looking at Newton's second law, which states that [tex]\vec{F} = \frac{d\vec{p}}{dt}[/tex], and so this immediately results in [tex]\Delta p = \int_{t_0}^{t_f}\vec{F} dt [/tex]
  6. Jan 23, 2016 #5
    Thank you!
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