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I have this confusion concerning distance and speed.

Typically, we express displacement and distance relative to a reference point, which we regard to be an unmoving location. As displacement has a direction, there is only one displacement. However, aren't there an infinite number of distances? If so, shouldn't speed, which is the rate of the change of distance have an infinite amount of possible values? (each value of speed will correspond to a certain distance)

But an object which has already moved will have followed a definite path and therefore would have a definite distance (and speed). If so, do we consider distances only for objects which have already moved? (thus, producing a definite distance)

By the way, what term do we use to refer to the rate of change of speed?(not velocity)

Thanks.

PS - Please write answers in a simple manner. I'm still new to physics

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You are overthinking this. Speed is rate of change of distance. Velocity is rate of change of displacement. Because distance and displacement are not necessarily the same, speed and velocity are not necessarily the same either. Yes, you are correct - many different distances could correspond to the same displacement, so one particular velocity could correspond to many possible speeds. But equally one particular distance could correspond to many different displacements. However, for any particular motion there is only one speed (not many) and one velocity.

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  • $\begingroup$ That resolved my problem. Thanks. And I think you meant "speed and velocity are not necessarily the same either" $\endgroup$ – SNB May 22 '16 at 3:03
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Calm down.

aren't there an infinite number of distances.

This Statement is necessarily false. Distance is an scalar and is unique with a magnitude.

It is true that that the possible distances are infinite but at a particular time (say t = 10 min) there will be an unique value of distance.

The answer to

what term do we use to refer to the rate of change of speed?(not velocity)

is that rate of change of speed is ambiguous. If your frame of reference or assumptions include an direction then it is acceleration.

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  • $\begingroup$ I am not sure what you are asking for, but maybe you will find some answers in Zeno's paradoxes of motion (google it) $\endgroup$ – user98038 May 19 '16 at 14:44

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