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There are many ways of looking at this question first and foremost you must state the position of your self with respect to the body. case 1 You are stationary or moving with a constant velocity. And located outside the object under consideration. In this case if the body has suffered from a change in velocity or a continued change in velocity or a change in direction or is currently changing its direction. It has undergone or is currently undergoing acceleration. case 2 You are located inside the body and the body is hollow and you are able to see what happens outside the body through a window like object or rather this case can be better explained if you imagine yourself sitting on the object while its in motion. Similarly here also change in velocity and direction can be marked although you will find the relative velocity between the two the object and you to be zero. Case 3 When you are inside the body,with no way to know how the body behaves in an external frame of reference. Also it may be noted that the body is hollow. Here whenever the body undergoes an acceleration you will sense it owing to your inertia.But if the body has undergone acceleration already and is now moving in a constant velocity there is no way of knowing the time or amount of acceleration it has undergone. Case 4 when you are inside a solid body with no way to look at an external frame of reference. Due to the nature of the body you cannot sense the effect of inertia. therefore one cannot sense whether the body is undergoing acceleration or has undergone acceleration in the past.

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Q: How can you tell that an object has undergrown acceleration?
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