The reason why the area under the graph of a positive velocity function gives the total distance that has been travelled.

Answer to Problem 1RWDT
It has been shown why the area under the graph of a positive velocity function gives the total distance that has been travelled.
Explanation of Solution
Given:
An arbitrary graph of a positive velocity function.
Concept used:
Distance travelled is the product of speed and time.
Calculation:
The difference between speed and velocity is that speed does not have a direction and is always positive, while velocity has direction and may be positive or negative.
This implies that a positive velocity function is nothing but a function which denotes the speed.
Now, for each small interval of time, the distance travelled is evaluated by multiplying the small interval of time and the velocity at that small interval of time, which tends to a constant value for sufficiently small intervals of time. Note that this value is nothing but the area of a small vertical strip under the graph.
Adding all such values for subsequent intervals of time, the total distance can be evaluated. On the other hand, geometrically, such a value is nothing but the total area under the graph.
This shows why the area under the graph of a positive velocity function gives the total distance that has been travelled.
Conclusion:
It has been shown why the area under the graph of a positive velocity function gives the total distance that has been travelled.
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