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9. A particle is moving on a line is at position s(1)=r' - 7²+8t-2 at time t. a) At what times is it at rest? b) At what times is it changing position?. c) When is it moving left and right? d) When is it speeding up and slowing down? e) What is its acceleration when t = 2? ) What is the total distance traveled from t= 1 to t= 5?

9. A particle is moving on a line is at position s(1)=r' - 7²+8t-2 at time t. a) At what times is it at rest? b) At what times is it changing position?. c) When is it moving left and right? d) When is it speeding up and slowing down? e) What is its acceleration when t = 2? ) What is the total distance traveled from t= 1 to t= 5?

College Physics
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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9. A particle is moving on a line is at position s(1)=-77+8t-2 at time t. a) At what times is it at rest? b) At what times is it changing position?. c) When is it moving left and right? d) When is it speeding up and slowing down? e) What is its acceleration when t = 2? f What is the total distance traveled from t= 1 to t= 5?
Transcribed Image Text:9. A particle is moving on a line is at position s(1)=-77+8t-2 at time t. a) At what times is it at rest? b) At what times is it changing position?. c) When is it moving left and right? d) When is it speeding up and slowing down? e) What is its acceleration when t = 2? f What is the total distance traveled from t= 1 to t= 5?
Expert Solution
Step 1

Given

Position of the particle at time t is

st=t3-7t2+8t-2  ---1

Then velocity is derivative of position with respect to time t

vt=dsdt

     =3t2-14t+8  ---2

Acceleration is derivative of velocity with respect to time t

at=dvdt

      =6t-14  ---3

     

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