(3) The graph shows the position curve for a particle moving along x-axis. (a) Describe the motion of the

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1 AS CALCULUS CHP, 2.2 PARTICLE MOTION WORKSHEET NAME DATE (1) Nolan Ryan, one of the fastest baseball pitchers of all time, was capable of throwing a baseball 150 ft/s ( over 102 mph). Could Nolan have hit the 208 ft ceiling of the Astrodome if he were gave the baseball an initial upward velocity of 100 fl/s from a height of 7 feet? What would be his maximum height? What is the average velocity of the baseball during time 1!~t!53 seconds of flight? (2) The graph shows the position graph for a particle moving along the x-axis. (a) What is the velocity of the particle? (b) What is position at time t'2? (c) Write the position-time function. :s) (ci) Graph velocity onto graph given: (3) The graph shows the position curve for a particle moving along x-axis. (a) Describe the motion of the *lcm.1 particle in words. It) j (b) Graph velocity, si (4) (1998 AB multiple choice) A particle moves along x-axis so that its position at time t is given by x(t) = t2-6t + 5. For what value oft is the velocity of the particle zero? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 t (5) The graph shows the time to distance graphof a 1996 Riley and Scott MK III-Olds WSC racecar.(a) In mph, what is the average 2 velocity on* t[2,5) seconds? I (b)estimate the velocity (mph)at t=2 seconds. Itsnn :. uaann, 1 RMflV! I, 00, fl -- ME I Elapsed time (sec)

2 (6) A student walks around in front Of a motion detector that records her velocity at itsecond intervals for 36 seconds as shown in velocity graph. Describe her motion as a function of time by reading the graph. When is her speed a maximum? [-4, 361 by 1-7-5, 7.51 (7) A particle moving along an x-axis with constant acceleration has velocity v=3 It/s at time t=1 and velocity v=-1 ft/s at time t4. (a) Find the acceleration of the particle. (b) Find an equation that expresses v as a function oft. (c) What is the velocity of the particle at time t=o? (8) The accompanying figure shows I kmlh) the velocity versus time curve for a particle moving along an x-axis. Describe the motion in words. r(h (9) The accompanying figure shows the position versus time curve for an elevator that moves upward a distance of GOm 60 and then discharges its passengers )) 6 21) H) Estimate the instantaneous velocity of the elevator at t= los. H) IS 2)) Time (s) 0

3 (10) A particle is moving along a straight line with the following distance - time graph. (a) Find the average velocity over t(0,31. (b) Find the values oft at which the instantaneous velocity is zero. (c) Find all values oft at which the instantaneous velocity is either a maximum or minimum. 0 I 2i flme s) (11) The graphs of three velocity functions are shown. In each case determine the sign of the acceleration, then determine whether the particle is speeding up or slowing down. (12) Match the following position functions with velocity functions. (ci) i/n 1(1 I I) 111i (III)

4 (13) Given the graph of velocity below, sketch a graph of (a) speed and (b) acceleration versus time. (0) t 2 34 (14) A projectile is fired vertically upward with an initial velocity of 49 meters per second from a tower 150 meters high. (a) How long will it take the projectile to reach its maximum height? (b) What is the maximum height? (c) How long will it take for the projectile to pass its starling point on the way down? (d) What is the velocity when it passes the starting point on the way down? (e) How long will it take the projectile to hit the ground? (1) What will be its speed at impact? (D

5 (15) Calvin and Phoebe are running side by side along the jogging trail. At time t0, each one starts speeding up. Their velocities are given by the following, where p(t) and c(t) are in feet per second and t in seconds. c(t) = 16-6(2) for Calvin p(t) = 10 + '11 for Phoebe (a) At time zero, are each going the same speed? Why? (b) What are the limits of their speeds as t approaches infinity? What is this surprising information telling you? (16)11 you place-kick a football, its displacement above the ground, d(t) meters, is given by d(t) = 18t - 4.9t2, where t is time in seconds since it was punted. (a) Find d'(l) and d'(3). (b) At times t=1 and t=3, is the football going up or down? (c) Find the velocity at t=4. Explain why the answer has a meaning in the mathematical world but not in the real world. Ol

6 (17) THE ROCKET PROBLEM When a model rocket is launched, the propellant bums for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for a while and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts downward. The parachute slows the rocket to keep it from breaking when it lands. This graph shows velocity data from the flight. Tune after launch (set) (a) How fast was the rocket climbing when the engine stopped? (b) For how many seconds did the engine burn? (c) When did the rocket reach its highest point? What was the velocity then? (d) When did the parachute pop out? How fast was the rocket falling then? (e) How long did the rocket fall before the parachute opened? (f) When was the rocket's acceleration greatest? When was the acceleration constant? rol