EXAMPLE 6 A particle moves along a line so that its velocity at time t is v(t) = t - t - 20 (measured in meters per second). (a) Find the displacement of the particle during 2 s t s 9. (b) Find the distance traveled during this time period. SOLUTION (a) By this equation, the displacement is s ( 9 ) - 5 ( 2 ) = V ( t ) at ( 12 - t - 20 ) at - 20t This means that the particle moved approximately 61.83 meters to the right. (b) Note that v(t) = t2 - t - 20 = (t - 5)(t + 4) and so v(t) [sv . 0 on the interval [2, 5] and v(t) [2 v . 0 on [5, 9]. Thus, from this equation, the distance traveled is -12 ( - 2 + + + 20 ) at + / ( 8 - t - 20 ) at Find the general indefinite integral. (Use C for the constant of integration.) 8x3 - 9Vx dx Evaluate the integral. 6 (2x - 3 ) (8x 2 + 9 )dx