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The position of a particle between t = 0 and t = 2.00 s is
Chapter 2, Problem 57P(choose chapter or problem)
Problem 57P
The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s3)t3 − (10.0 m/s2)t2 + (9.00 m/s)t. (a) Draw the x-t, υx-t, and ax-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 υx−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 ax(t) and from the υx−1 graph. (d) At what time(s) between t = 0 and t = 2.00 s is the velocity of the particle instantaneously not changing? Locate this point on the υx-t and ax-t graphs of part (a). (e) What is the particle’s greatest distance 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 υx-t and ax-t graphs of part (a).
Questions & Answers
QUESTION:
Problem 57P
The position of a particle between t = 0 and t = 2.00 s is given by x(t) = (3.00 m/s3)t3 − (10.0 m/s2)t2 + (9.00 m/s)t. (a) Draw the x-t, υx-t, and ax-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 υx−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 ax(t) and from the υx−1 graph. (d) At what time(s) between t = 0 and t = 2.00 s is the velocity of the particle instantaneously not changing? Locate this point on the υx-t and ax-t graphs of part (a). (e) What is the particle’s greatest distance 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 υx-t and ax-t graphs of part (a).
ANSWER:
Solution 57P
Step 1:
Given data
The position of a particle x(t) = (3.00 )
− (10.0
)
+ (9.00
) t.
Time t = 0 and 2s
Problem (a)
To draw the graphs of the particle