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Delivation of v=u+at in physics?

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Delivation of v=u+at in physics?

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  1. So I think you might be asking Derivation of v = u + at

    I'm not sure what u represents but it must be some sort of velocity term so I think you mean this

    Vf = Vi + at

    This equation only works at constant acceleration or if you are given the average acceleration OR if you calculate the average acceleration by (af + ai)/2. (af + ai)/2 only works when the super acceleration is constant (super acceleration is the change in acceleration).

    Really all the equation says is:

    Change in V = (average a)*t

    There are way to derived it through calculus which requires differentiating position. Really though, the equation is pretty intuitive as is.


  2. assume,

    u=initial velocity

    v= final velocity

    then the acceleration of the body in the time t is given by

             a=(v-u)/t

             v-u=at

             v=u+at

  3. according to definition of acceleration,

    acceleration=rate of change of velocity per unit time

    therefore

    a=dv/dt

    or

    dv=a.dt

    now integrating on both sides from velocity u to v and time 0 to t

    v-u=at

    or v =u+at

  4. Hi,

    It's actually an integral. You may not have done them yet ...you will near the end of high school most likely.

    Let s(t) represent the displacement of a particle at time t.

    Then ds/dt is the velocity v(t) (ds/dt is a rate of change ...if s were a linear or straight line graph ds/dt would just be the slope ...if s(t) were a curve, then ds/dt at a point t_0 would represent the slope of a tangent line at t_0 or the velocity of the particle at t=t_0)

    The acceleration of the particle (actually the vector component along an axis of your choice) ...is d^2s/dt^2=a(t)

    Think of it as the slope of the velocity graph ....

    now integrating a(t)dt

    we get v(t) = A(t)+C

    so if a(t) were constant call it a

    then v(t) = at +C where C is the initial velocity and a is the constant accleration ...that comes from integrating

    INTEGRAL[ a*dt] =at+C =v(t)

    check the units too ...and you can see a is in m/s^2

    so m/s^2 * s = m/s

    and C is in m/s so it works out

    I hope it helps

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