Problem 1. If you know the position vectors of a particle at two points along its path and also know the time interval during which it moved from one point to the other, can you determine the particle's instantaneous velocity? Its average velocity? Its average or instantaneous acceleration? Explain you answers. Problem 2. Construct diagrams showing the velocity and acceleration of a projectile at several points along its path assuming, (a) it was launched horizontally and (b) it was launched at an angle above the horizontal. Problem 3. A fish swimming in a horizontal plane has velocity v₁ = (4+) m/s at a point in the ocean where the position relative to a rock is r₁ = (104) m. After the fish swims with a constant acceleration for 20 s, its final velocity is = (2015) m/s. (a) What are the components of its acceleration? (b) What is the direction of its acceleration with respect to the unit vector i? (c) If the fish maintains this constant acceleration, where is it at t = 25 s, and in what direction is it moving? Problem 4. A particle starts from the origin with velocity 51 m/s at t = 0 and moves in the xy plane with a varying acceleration given by a = 6√√tj m/s², where t is in s. (a) Determine the vector velocity of the particle as a function of time. (b) Determine the displacement of the particle as a function of time.