2. Given two matrices, determine AB and BA. Is AB = BA? 3. The position of a particle is given by = 6. A-134-431,8-13113| where a is a constant. Find the velocity and sketch the trajectory. (Hint: In sketching the motion of a particle, it is usually helpful to look at limiting cases as t 0 and as t - 00.) 4. The position of a particle at any time t is given by x = a, y = bt², where a and b are constants. Find the rectangular and polar components of its velocity and acceleration (a) at any time t, (b) when a = 12 cm, b= 1 cm/s², and when t = 3 s. 7. Floor 5. A particle moves along a space curve C with a vector is given by r(t) = 3 cos cos 2t e, + 3 sin sin 2t e₂ + (8t - 4), a. Find a unit tangent vector T to the curve C. b. Show that v=vT A particle moves at a constant acceleration along the curve x₂ = x/100 from point A to point B. The velocity of the particle at A is 10 m/s, and 10 s later, at point B it is traveling at 50 m/s. Determine the total acceleration of the particle at point B. Show that finite rotation is not a vector quantity.

2. Given two matrices, determine AB and BA. Is AB = BA? 3. The position of a particle is given by = 6. A-134-431,8-13113| where a is a constant. Find the velocity and sketch the trajectory. (Hint: In sketching the motion of a particle, it is usually helpful to look at limiting cases as t 0 and as t - 00.) 4. The position of a particle at any time t is given by x = a, y = bt², where a and b are constants. Find the rectangular and polar components of its velocity and acceleration (a) at any time t, (b) when a = 12 cm, b= 1 cm/s², and when t = 3 s. 7. Floor 5. A particle moves along a space curve C with a vector is given by r(t) = 3 cos cos 2t e, + 3 sin sin 2t e₂ + (8t - 4), a. Find a unit tangent vector T to the curve C. b. Show that v=vT A particle moves at a constant acceleration along the curve x₂ = x/100 from point A to point B. The velocity of the particle at A is 10 m/s, and 10 s later, at point B it is traveling at 50 m/s. Determine the total acceleration of the particle at point B. Show that finite rotation is not a vector quantity.