APPM 1345 Midterm: appm134spring2013exam2_sol
Document Summary
Spring 2013: (22 points) the velocity function (in meters/second) for a particle moving along a line is v(t) = 8 t3. Solution: (a) z v(t) dt = z (cid:0)8 t3(cid:1) dt = 8t t4. 0 (cid:0)8 t3(cid:1) dt = 8t t4. = 8(4) 64 0 = 32 64 = 32 (c) first determine that v(t) = 8 t3 = 0 at t = 2. = |8(2) 4 0| + |8(4) 64 (8(2) 4)| = 12 + | 32 12| = 12 + 44 = 56 (d) from part (b) we know that z 4. 4 ( 32) = 8 (e) the mean value theorem states that there is a c in [0, 4] such that v(c) = vave. 8 c3 = 8 c3 = 16 c = 3 16 = 2 3 2 (f) the displacement equals z 4 (g) the distance traveled equals z 4. 0 v(t) dt = 32 (from part (b)).
