Answer with solution

ASSESSMENT 5.1: VELOCITY AND ACCELERATION Specific Directions: In each of the following, do as told. 1. Ifs = t3 - 5t2 + 5t - 3, when will the velocity be 2? 2. If s = t2 - +3, find the velocity when the acceleration is zero? 3. Two particles have positions at time t given by the equations s, = 4t - t2 and $2 = t2 - 2. Find their positions when they have the same velocity. 4. Two particles have positions at time t given by the equations s, = 4t -t2 and $2 = 6t2 - +3. Find their velocities when they have the same acceleration. 5. A cliff 128 feet high overhangs a lake. A man on the edge of the cliff throws a stone vertically upward with a velocity of 32 feet per second. At what velocity does the stone strike the water? ASSESSMENT 5.2: MAXIMA AND MINIMA; CRITICAL POINTS Specific Directions: Indicate the maximum and minimum points in Items 1, 2 and 3; for Items 4 and 5, do as told. 1. y = x2 - 4x - 1 2. y = 2x3 - x2 + 3x - 1 3. y= x+x1 4. Find a and b so that the curve y = ax + bx" will have a critical point at (2,4). 5. Find a and b so that the curve y = x3 + ax? + b will have a critical point at (2,5)