1. 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} 1. 2.
v ( t ) = {image} 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

2. 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} 1. 2.
|v ( t )| = {image} 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

3. Find the position vector of a particle that has the given acceleration and the given initial velocity and position. a ( t ) = - 4 k, v (0) = i + j - 3 k, r (0) = 10 i + 8 j 1.
r ( t ) = {image} 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

4. What force is required so that a particle of mass m has the following position function? r ( t ) = {image} 1.
F ( t ) = 60 t i + 14 j + 54 t k
F ( t ) = {image}
F ( t ) = m (60 t i + 14 j + 54 t k) 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

5. A ball is thrown at an angle of 15 {image} to the ground
A ball is thrown at an angle of 15 {image} to the ground. If the ball lands 150 m away, what was the initial speed of the ball? Here g = 9.8 {image} . 1. 2.
v0 {image} 27.1 m/s
v0 {image} 18.1 m/s
v0 {image} m/s
v0 {image} 54.2 m/s 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