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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## Tuesday, September 16, 2008

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