i beg you guys i really need help with this A particle moves according to a law of motion \( s = f(t), \, t \geq 0 \), where \( t \) is measured in seconds and \( s \) in feet. (If an answer does not exist, enter DNE.)1. \( f(t) = t^3 - 2t^2 - 24t \) (a) Find the velocity at time \( t \). \( v(t) = \) (b) What is the velocity after 1 second? \( v(1) = \) ft/s (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total distance traveled during the first 6 seconds. Answer: (f) Draw a diagram like this figure to illustrate the motion of the particle. Diagrams: - From \( t = 0 \) to \( t = 3 \), \( s = 0 \) to \( s = -\frac{108}{27} \) - From \( t = 3 \) to \( t = 4 \), \( s = -\frac{108}{27} \) to \( s = 0 \) - From \( t = 4 \) to \( t = 6 \), \( s = 0 \) to \( s = 90 \)2. (g) Find the acceleration at time \( t \) and after 1 second. \( a(t) = \) \( ft/s^2 \) \( a(1) = \) \( ft/s^2 \)3. (h) Graph the position, velocity, and acceleration functions for \( 0 \leq t \leq 6 \). (A graphing calculator is recommended.) Graphs show: - Position, velocity, and acceleration as curves over the interval \( 0 \leq t \leq 6 \). - The curves demonstrate the changes over time with respective axes marked appropriately.4. (i) When is the particle speeding up? (Enter your answer using interval notation.)5. (j) When is it slowing down? (Enter your answer using interval notation.)This exercise encompasses the analysis of motion, focusing on calculating velocity,

(a) ind the valocity at timet () What is he veleeity after econd? (e) whan is e partie at ret? (4) When i the particle moving in the positive direction? (Enter your anewer ueing interval natation.) (e) nind the total dintance traveled during the firet 6econde O) Draw a diagmm like thie figure to illuntrate the mation of the particie. IRAR (a) rind the acceleration at time tand after i econd. () Graph the poetion, velacity, and sccelestion functione for ostaE. (A graphing caiculator i recommended.) 100 100 20 20 O- 00 When i thn particle peeding up? (Enter your anwer uning interal notation.) When t slowing down? (Enter your anwer uning interval notation.)

(a) ind the valocity at timet () What is he veleeity after econd? (e) whan is e partie at ret? (4) When i the particle moving in the positive direction? (Enter your anewer ueing interval natation.) (e) nind the total dintance traveled during the firet 6econde O) Draw a diagmm like thie figure to illuntrate the mation of the particie. IRAR (a) rind the acceleration at time tand after i econd. () Graph the poetion, velacity, and sccelestion functione for ostaE. (A graphing caiculator i recommended.) 100 100 20 20 O- 00 When i thn particle peeding up? (Enter your anwer uning interal notation.) When t slowing down? (Enter your anwer uning interval notation.)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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