Q) A bird flies with a speed of v=| t-2 | m/s along a straight line , where t is in seconds. Find the distance traveled by the bird during the first 4 seconds of motion.

A) v = | t-2 | m/s
The critical point is t = 2 (At which the modulus becomes 0)
so from t=0 to t=2 , velocity is (t-2) m/s
and from t=2 to t= 4, velocity is (2 - t) m/s
Total distance covered = mod of ( integral (0 to 2) [ t-2] + integral (2 to 4) [ 2 - t] )
= [t^2/2 - 2t] 0 to 2 + [ 2t - t^2/2] 2 to 4
= | -2 - 2 |
= |-4 |
= 4 m
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