University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2021
Views:

160

Pages:

6
Author:

Adriel Kelley

AP Calculus AB Name Key Rectilinear and Projectile Motion Worksheet #2 The position of a skateboarder at any time t (in seconds) is given by the function (s(t) = t^3 - 8t^2 + 8t) measured in feet. a) What are the velocity and acceleration functions in terms of t? b) When is the skateboarder at rest? c) What is the position(s) of the skateboarder when at rest? d) What are the position, velocity, and acceleration of the skateboarder at three seconds and at 5 seconds? e) Sketch a motion schematics for the skateboarder. Make sure to label position and velocity at each critical time. f) What was the total distance traveled in the first five seconds? g) Find the displacement in the first 5 seconds. h) When is the skateboarder moving to the right and left? Use interval notation for your answers. a) (v(t) = 3t^2 - 16t + 8) (a(t) = 6t - 16) b) (0 = 3t^2 - 16t + 8) (t = .558) sec (t = 4.775) sec c) (s(.558) = 2.147) ft. (s(4.775) = -35.332) ft. d) (s(3) = -21) ft (\qquad s(5) = -35) ft (v(3) = -13) ft/sec (\qquad v(5) = 3) ft/sec (a(3) = 2) ft/sec² (\qquad a(5) = 14) ft/sec² e) [Motion schematic sketch] (t = 4.775) (s = -35.332) (v = 0) (t = .558) (s = 2.147) (v = 0) (t = 0) (s = 0) (v = 8) f) (s(0) = 0 \qquad s(.558) = 2.147 \qquad s(4.775) = -35.332 \qquad s(5) = -35) (|2.147| + |-37.479| + |332| = 39.958) ft. g) (s(5) - s(0)) (-35 - 0 = -35) ft. 35 ft. to the left. h) left: ((.558, 4.775)) right: ([0, .558) \cup (4.775, \infty)) The position of a particle at any time t (in seconds) is given by the function (s(t) = 2t^3 - 27t + 15) measured in feet. a) What are the velocity and acceleration equation in terms of t? b) When is the particle at rest? c) What is the position(s) of the particle when it is at rest? d) What are the initial position, velocity, and acceleration of the particle? e) Sketch a motion schematics for the skateboarder. Make sure to label position and velocity at each critical time. f) What is the total distance traveled from one second to six seconds? g) What is the displacement for the same time frame? h) When is the particle moving to the left and right? Use interval notation for your answers. a) (v(t) 1 = 6t^2 - 27) (a(t) = 12t) 1. www.cbsd.org www.cbsd.org b) (0 = 6t^2 - 27) (27 = 6t^2) (\lceil t^2 = \sqrt{4.5}) (t = 2.121) sec c) (s(2.121) = -23.184) ft. d) (s(0) = 15) ft (v(0) = -27) ft/sec (a(0) = 0) ft/sec² e) [Motion schematic sketch] (t = 2.121) (s = -23.184) (v = 0) (t = 0) (s = 15) (v = -27) f) (s(1) = -10) (s(6) = 285) (|-13.184| + |308.184| = 321.368) ft. g) (s(6) - s(1)) (285 - (-10)) (295) ft. h) left: ([0, 2.121)) right: ((2.121, \infty))