Find the velocity of a particle with the given position function

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Find the velocity of a particle with the given position function Find the velocity of a particle with the given position function. r (t) = {image} v ( t ) = {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the speed of a particle with the given position function Find the speed of a particle with the given position function. r ( t ) = {image} |v ( t )| = {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the position vector of a particle that has the given acceleration and the given initial velocity and position. a ( t ) = - 6 k, v (0) = i + j - 8 k, r (0) = 8 i + 2 j r ( t ) = {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

F ( t ) = m (30 t i + 6 j + 36 t k) F ( t ) = {image} What force is required so that a particle of mass m has the following position function? r ( t ) = {image} F ( t ) = m (30 t i + 6 j + 36 t k) F ( t ) = {image} F ( t ) = 30 t i + 6 j + 36 t k 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50