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What will be the velocity-distance graph of constant acceleration?

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What will be the velocity-distance graph of constant acceleration?

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  1. it should be exponentially going upwards--similar to half a 'U' or a 'J'


  2. acceleration is defined as the time derivative of velocity, dv/dt

    if it is constant acceleration, then dv/dt = constant

    constant slope = linear /straight line

    intuitively, if it was exponential, with distance on the x axis, then the faster you were travelling, the less distance youd be covering!!!

    Arguing that the relationship is anything but linear is stating that the velocity is changing at a continually different rate, which negates the assumption of constant acceleration.

  3. It'll be a straight line, not parallel to either axis.

    I mean, a straight line, passing through origin. This is because constant acceleration mean regular change of velocity.

  4. Distance is the integral of velocity (area). Acceleration is the differential of velocity (slope). Now, you know you have a constant acceleration, lets make it C. To go from constant acceleration to speed, you integrate C. Thus getting C(t) m/s, where t is time. Distance is yet another integral, but of velocity which we know is C(t). So for distance you have 1/2C(t)p2. So to graph velocity against distance, you must take into account, that distance changes with the power of 2 of time, and velocity to the power of one of time. Thus, on the graph, the slope will start high, and then in a exponential curve slow down as you move on the distance axis.

  5. For constant acceleration

    v^2 = u^2 + 2as

    The graph goes exponentially upward.

  6. The graph should be a straight line.  

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