Question 1:

EXAMPLE 6 A particle moves along a line so that its velocity at time t is v(t) = tz - t - 6 (measured in meters per second). (a) Find the displacement of the particle during 1 s t s 6. (b) Find the distance traveled during this time period. SOLUTION (a) By this equation, the displacement is s (6 ) - s(1 ) = v( t ) at (1 2 - t - 6 ) at co co t2 16 6t 24.17 X This means that the particle moved approximately 24.17 meters to the right. (b) Note that v(t) = t2 - t - 6 = (t - 3)(t + 2) and so v(t) s v 0 on the interval [1, 3] and v(t) 2 v 0 on [3, 6]. Thus, from this equation, the distance traveled is (-2 + + + 6 ) at+ / ( 2 - t - 6 ) at 3 + + 6t + Co 3 N TO - 6t = 38.83 X