A bird files with a speed $v=\left| t-2 \right| \;m/{ s}$ along a straight line, where $t$ is the time in seconds. The distance travelled by the bird during first four seconds is equal to

The distance traveled is found by integrating the velocity function, v = |t-2|, from t = 0 to t = 4 seconds. Using the area under the curve method for the piecewise function, we evaluate the integral separately from 0 to 2 (where v = 2-t) and 2 to 4 (where v = t-2). The calculation is [(2t - t^2/2) from 0 to 2] + [(t^2/2 - 2t) from 2 to 4], which equals (4 - 2) + (8 - 8 - (2 - 4)) = 2 + 2. The total distance travelled by the bird during the first four seconds is 4 m.

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