2.57 • CALC The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s³)r³ – (10.0 m/s²)t² + (9.00 m/s)t. (a) Draw the x-t, v,-t, and a,-t graphs of this particle. (b) At what time(s) between t = 0 and t = 2.00 s is the particle instantaneously at rest? Does your numerical result agree with the v,-t graph in part (a)? (c) At each time calculated in part (b), is the acceleration of the particle positive or negative? Show that in each case the same answer is deduced from a,(1) and from the v,-t graph. (d) At what time(s) between 1 = 0 and t = 2.00 s is the velocity of the particle instantaneously not changing? Locate this point on the Vg-t and a,-t graphs of part (a). (e) What is the particle's greatest dis- tance from the origin (x = 0) between t = 0 and t = 2.00 s? (f) At what time(s) between t = 0 and t = 2.00 s is the particle speeding up at the greatest rate? At what time(s) between t = 0 and t = 2.00 s is the particle slowing down at the greatest rate? Locate these points on the v,-t and a,-t graphs of part (a).

2.57 • CALC The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s³)r³ – (10.0 m/s²)t² + (9.00 m/s)t. (a) Draw the x-t, v,-t, and a,-t graphs of this particle. (b) At what time(s) between t = 0 and t = 2.00 s is the particle instantaneously at rest? Does your numerical result agree with the v,-t graph in part (a)? (c) At each time calculated in part (b), is the acceleration of the particle positive or negative? Show that in each case the same answer is deduced from a,(1) and from the v,-t graph. (d) At what time(s) between 1 = 0 and t = 2.00 s is the velocity of the particle instantaneously not changing? Locate this point on the Vg-t and a,-t graphs of part (a). (e) What is the particle's greatest dis- tance from the origin (x = 0) between t = 0 and t = 2.00 s? (f) At what time(s) between t = 0 and t = 2.00 s is the particle speeding up at the greatest rate? At what time(s) between t = 0 and t = 2.00 s is the particle slowing down at the greatest rate? Locate these points on the v,-t and a,-t graphs of part (a).

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section2.1: Average Velocity

Problem 2.1QQ: Under which of the following conditions is the magnitude of the average velocity of a particle...

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