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Is it possible for a solid real world object to instantly gain speed without having to accelerate from $v = 0 \, \text{m/s}$ to $v = 1000\,\text{m/s}$, or does it have to accelerate in order to reach that speed? In other words (after some feedback from comments) is infinite acceleration physical?

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    $\begingroup$ What do you think? $\endgroup$
    – DanielSank
    Dec 30, 2016 at 2:13
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    $\begingroup$ Remember your kinematics equations, especially $v_f=v_i+a\Delta t$ $\endgroup$
    – Kyle Kanos
    Dec 30, 2016 at 2:14
  • $\begingroup$ Your question can be read as asking if a solid real world object can change speed without changing speed. Is this what you intend to ask? $\endgroup$ Dec 30, 2016 at 2:28
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    $\begingroup$ You're asking if infinite acceleration is physical? $\endgroup$ Dec 30, 2016 at 2:54
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    $\begingroup$ Then you are asking if infinite acceleration is physical. $\endgroup$ Dec 30, 2016 at 4:03

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Any solid real world object obeys the laws of classical physics. It is impossible for a solid real world object to gain speed without accelerating.

Consider the example of a car. The only ways to reach higher speeds in the car is if the driver steps on the gas pedal very hard or a collision with another object (like a moving car) such that the force exerted on it causes it to accelerate to a higher speed (via F = ma and kinematic equations). There is no force (nor gas pedal) strong enough to instantaneously change the speed of the car to its final speed from its initial speed.

Now consider another example. Just because light traveling over a short period of time appears to travel instantaneously to a nearby observer does not mean that light travels infinitely fast. Similarly, just because an object appears to have a much greater final speed relative to its initial speed does not mean that the object instantaneously reached its final velocity, but rather that it accelerated by a large finite amount over a short finite time interval.

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Kinematics equation for velocity is v=u+at which clearly states that without any acceleration v=u,so the speed will be same.

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