EXAMPLE 6 A particle moves along a line so that its velocity at time t is v t t t 6 measured in meters per second a Find the displacement of the particle during 1 t 6 b Find the distance traveled during this time period SOLUTION a By this equation the displacement is s 6 s 1 L v foce Live v t dt t t 6 dt v t dt coco This means that the particle moved approximately 24 17 meters to the right b Note that v t t t 6 t 3 t 2 and so v t s 0 on the interval 1 3 and v t 0 on 3 6 Thus from this equation the distance traveled is 1 1 2 620 v t dt Lovce v t dt 2 x 6 a 2 t dt t t 6 dt