Pre-Calc Homework Solutions 290

Pre-Calc Homework Solutions 290 - 290 Section 7.1 4. (a)...

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Unformatted text preview: 290 Section 7.1 4. (a) Right when 0, i.e., 0, v(t) 6t 2 18t t t 2) 12 6(t 1)(t 2) 1)(t 0, 2) 0, Section 7.1 Exercises 1. (a) Right when v(t) when 0 i.e., when t 2 2 0, which is when cos t or i.e., when t (b) Displacement 2 3 t 2 . Left when cos t 2 3 t . Stopped when cos t 0, 2 3 or . 2 2 i.e., when 0 i.e., when 1 6(t 1)(t 1. Left when 6(t 2. Stopped when 0, i.e., when x 2 1, or 2. 12) dt (b) Displacement 0 (6t 2 2 0 18t [(16 2 5 cos t dt 0 2 5 sin t 0 5[sin 2 sin 0] 0 2t 3 (c) Distance 9t 2 2 12t 6t 2 18t 12) dt 36 24) 0] 4 (c) Distance /2 0 0 5 cos t dt 3 /2 2 12 dt 2 1 1 0 5 cos t dt /2 5 cos t dt 3 /2 5 cos t dt (6t 2 1 18t 6 ( 6t2 18t 12) dt 0 5 10 5 20 0, which is when sin 3t 3 5 2. (a) Right when v(t) i.e., when 0 3 0, 5. (a) Right when v(t) cos t 0, which is when sin t t 3 or 2 2 0 and t 2 t . Left when sin 3t 0, i.e., when 0 0, i.e., when 0 0 and cos t 2 . Left t 0, or t 3 2 . Stopped when sin 3t 0, i.e., when t when sin t t 0, i.e., when or . /2 (b) Displacement 0 6 sin 3t dt cos 0 /2 6 1 cos 3t 3 /2 0 3 . Stopped when sin t 2 3 i.e., when t 0, , , , or 2 . 2 2 2 0 or cos t 2 cos (c) Distance /3 0 3 2 2 (b) Displacement 0 5 sin2 t cos t dt 5 1 sin3 t 3 2 0 5[0 6 sin 3t dt /2 0] 2 0 5 sin2 t cos t dt 3 /2 /2 0 6 sin 3t dt /3 6 sin 3t dt 49 9.8t 4 2 6 t 5. (c) Distance /2 0 0 3. (a) Right when v(t) Left when 49 0, i.e., when 0 t 10. 5. 5 sin2 t cos t dt 2 3 /2 5 sin2 t cos t dt 9.8t 0, i.e., when 5 9.8t 0, i.e., when t 5 sin2 t cos t dt 5 3 20 3 Stopped when 49 10 5 3 10 3 (b) Displacement 0 (49 10 9.8t) dt 10) 0] 0 6. (a) Right when v(t) when 0 t 0, which is when 4 4 t 0, i.e., t cannot be 4. 4 0 4. Left: never, since t t dt 49t (c) Distance 5 4.9t 2 10 49[(10 0 negative. Stopped when 4 4 0, i.e., when t 2 (4 3 49 0 9.8t dt 10 (b) Displacement ( 49 9.8t) dt 0 4 16 3 t)3/2 (49 0 9.8t) dt 5 122.5 122.5 245 2 [0 3 8] 4 (c) Distance 0 4 t dt 16 3 ...
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