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Math Help - non uniform acceleration

  1. #1
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    non uniform acceleration

    I have the following question,

    A car starts from rest and moves in a straight line in the manner descibed below:

    Period 1 0 to 4s the acceleration is non uniform i.e after 1s the aceleration is 1m/s after 2 secs the aceleration is 2m/s

    period 2 t=4-6 the velocity is constant

    period 3 from t=6-10 the car brakes uniformly to rest

    calculate the total distance the car travelled after 10 secs

    I can work out period 2 and 3 but theres nothing in my book about non uniform acceleration.


    any help you can give would be appreciatted
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  2. #2
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    Period 1 0 to 4s the acceleration is non uniform i.e after 1s the aceleration is 1m/s after 2 secs the aceleration is 2m/s
    no other info about about the interval t = 0 to t = 4 other than v(0) = 0 and the above?

    there are many models for non-uniform acceleration that one can come up with to fit the given data ...

    here's a simple one

    a(t) = t  \,\,, \,\, 0 \leq t < 4

    I'm sure that someone else can come up with other models for acceleration that will fit.
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  3. #3
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    Thats all the information given in the question, forgive me, but i cant understand how to use what you given me
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  4. #4
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    in the interval, 0 \leq t < 4 , if a(t) = t and v(0) = 0, then you can come up with a velocity function for that time interval.

    v(t) = \int t \, dt

    v(t) = \frac{t^2}{2} + C

    since v(0) = 0 ...

    v(t) = \frac{t^2}{2} \, \, , \, \, 0 \leq t < 4


    on the interval, 4 \leq t < 6 ... (velocity is constant)

    v(t) = 8


    on the interval, 6 \leq t \leq 10

    v(t) = 20 - 2t


    total distance traveled ...

    d = \int_0^4 \frac{t^2}{2} \, dt + \int_4^6 8 \, dt + \int_6^{10} 20-2t \, dt
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  5. #5
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    got it now! thanks
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