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Building up to understand integrals/area under curve.

  1. Aug 17, 2012 #1
    1. The problem statement, all variables and given/known data


    A particle starts at rest, then accelerates at a constant rate of 1 meter per second squared.


    2. Relevant equations


    Perhaps a(t) = t


    3. The attempt at a solution


    I have a series of calculus-related questions based on this statement, but first, I just want to know if the equation above, a(t)=t, and the graph below correctly represents the statement, "A particle starts at rest, then accelerates at a constant rate of 1 meter per second squared."


    integralgraph.png


    EDIT:

    Or, is the correct equation for the statement: a(t) = 1

    and the graph for the statement:

    integralgraph1.png
     
    Last edited: Aug 17, 2012
  2. jcsd
  3. Aug 17, 2012 #2
    Yes your second graph/equation is correct. Your first graph is the correct graph for the velocity of the particle. I don't know how much calculus you know already, but acceleration is the derivative of velocity, so you can get your second graph by differentiating the first.
     
  4. Aug 18, 2012 #3
    What you are asking is to solve the second-order differential equation [itex]\displaystyle \frac{d^2 y}{dt^2}=1[/itex]. Luckily for you, solving this differential equation requires near to no work compared to other second-order equations.

    What you do is to take the integral of the right hand side twice. You will end up with a function involving two constants because you are integrating twice. You can then find those constants giving the starting velocity and the starting position some values.

    And about your graph, the second one represents the acceleration. What does the first one represent?
     
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