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Find Velocity given Force and Mass

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data

    A 4.80 kg object initially at rest at the origin is subjected to the time-varying force shown in the figure

    What is the object's velocity at t =6 s ?

    2. Relevant equations

    F = ma ????????

    3. The attempt at a solution

    I guessed that the answer was 4.17 m/s (by doing a lot of googling), which was correct but i have no idea how to do this problem if it were on a test.
     

    Attached Files:

  2. jcsd
  3. Mar 17, 2009 #2
    Well, There is a formula which states that

    [tex]v=at[/tex]

    where v is the final velocity, a is the (average) acceleration and t is the time the body accelerates.

    This is a pretty intuitive formula if you think a little bit about it. The acceleration is unknown, but you can express it in terms of F and m (since you know that [tex]F=ma[/tex])

    Combining these gives

    [tex]v_{final}=\frac{F}{m} t[/tex]

    This we can write as

    [tex]v_{final}=\frac{Ft}{m}[/tex]

    [tex]Ft[/tex] represents the integral (area under the graph) from 0-4 seconds. If/after you study more differential math this will also be intuitive.

    Does this help?

    Notice that the body doesn't accelerate after 4 seconds, since no force acts on it, and thus its speed stays constant. In other words the body has the same speed at 4 seconds and 6 seconds (if opposing forces are assumed to be small)
     
    Last edited: Mar 17, 2009
  4. Mar 17, 2009 #3

    tiny-tim

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    Hi alexas! :smile:

    I assume you knew that F = ma, or force = mass times acceleration, and so you could get the acceleration from the graph by dividing by 4.8

    ok … draw a new graph (in your mind, if you like) …

    it has acceleration against time …

    how can you find the velocity just by looking at that graph? :smile:
     
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