# Answer to Question #29381 in Mechanics | Relativity for Riyank

Question #29381

Slope of distance time graph of moving body is given as speed and slope of displacement-time graph of moving body is given as velocity. Justify ?

Expert's answer

A slope of any graph y(x) is the derivative of that functiondy/dx.

If we have a distance-time graph, s(t), its slope is ds/dtwhich essentially is an increment of distance divided by the corresponding

increment of time, which is the speed by definition. The traveled distance, and the speed, can be only positive(zero or above). The displacement, on the other hand, can be either positiveor negative with reference to some origin point. The velocity is the derivative of displacement over time and it can have both signs as well.

If we have a distance-time graph, s(t), its slope is ds/dtwhich essentially is an increment of distance divided by the corresponding

increment of time, which is the speed by definition. The traveled distance, and the speed, can be only positive(zero or above). The displacement, on the other hand, can be either positiveor negative with reference to some origin point. The velocity is the derivative of displacement over time and it can have both signs as well.

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