Repeating the same argument for each thin rectangle, we come to the conclusion that the total distance covered during the time interval (o,t) is equal to the area of the staircase or, in the limit, to the area of the triangle ABC.

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We now can replace the smooth slope corresponding to the continuous motion of the object with a kind of staircase representing a jerky motion in which the velocity abruptly changes by small increments and remains constant for a short time until the next jerk takes place.