Schaum's Outline of Theory and Problems of Beginning Calculus

CHAP. 181 RECTILINEAR MOTION AND INSTANTANEOUS VELOCITY 141The car is never at rest. It makes sense to talk about the car being at rest only when the position of thecar is constant over an interval of time (not at just a single point). In such a case, the velocity would be zeroon an entire interval.Supplementary Problems18.4 (a) If an object is released from rest at any given height, show that, after t seconds, it has dropped 16t2 feet(assuming that it has not yet struck the ground).(b) How many seconds does it take the object in part (a) to fall: (i) 1 foot; (ii) 16 feet; (iii) 64 feet; (iv) 100feet?185 A rock is dropped down a well that is 256 feet deep. When will it hit the bottom of the well?18.6 Assuming that one story of a building is 10 feet, with what speed, in miles per hour, does an object droppedfrom the top of a 40-story building hit the ground?18.7A rocket is shot straight up into the air with an initial velocity of 128 feet per second.(a) How far has it traveled in 1 second? in 2 seconds? (b) When does it reach its maximum height? (c) Whatis its maximum height? (d) When does it hit the ground again? (e) What is its speed when it hits theground ?18.8 A rock is thrown straight down from a height of 480 feet with an initial velocity of 16 feet per second.(a) How long does it take to hit the ground? (b) With what speed does it hit the ground? (c) How long doesit take before the rock is moving at a speed of 112 feet per second? (d) When has the rock traveled adistance of 60 feet?18.93An automobile moves along a straight highway, with its position given by s = 12t3 - 18t2 + 9t - -2[s in miles, t in hours].(a) Describe the motion of the car: when it is moving to the right, when to the left, where and when itchanges direction.(b) What distance has it traveled in 1 hour from t = 0 to t = l?18.10 The position of a moving object on a line is given by the formula s = (t - l)3(t - 5).(a) When is the object moving to the right? (b) When is it moving to the left? (c) When is it changingdirection? (d) When is it at rest? (e) What is the farthest to the left of the origin that it moves?18.11 A particle moves on a straight line so that its position s (miles) at time t (hours) is given bys = (4t- 1Kt - 1)2.(a) When is the particle moving to the right? (b)' When is the particle moving to the left? (c) When does itchange direction? (d) When the particle is moving to the left, what is the maximum speed that it achieves?(The speed is the absolute value of the velocity.)18.12 A particle moves along the x-axis according to the equation x = 10t - 2t2. What is the total distancecovered by the particle between t = 0 and t = 3?18.13 A rocket was shot straight up from the ground. What must have been its initial velocity if it returned toearth in 20 seconds?