Next, we must find the total distance traveled by the particle in the given time interval. This is different than displacement, which only measures the difference between the beginning and end points. There may be positive distance and negative distance traveled that cancel each other out in the net change. Recall that when v(t) s 0, the particle moves to the left, and when v(t) 2 0, the particle moves to the right. Therefore, to calculate the total distance traveled, we must integrate the absolute value of velocity, Iv(t)l. First, find the values of t such that v(t) s o. v(t) so 9t - 4 S0 Therefore, Iv(t)I = -v(t) when v(t) is negative, which within the given time interval is 0 sts Similarly, Iv(t)| = v(t) when v(t) is positive, which within the given time interval is ses 3.
Next, we must find the total distance traveled by the particle in the given time interval. This is different than displacement, which only measures the difference between the beginning and end points. There may be positive distance and negative distance traveled that cancel each other out in the net change. Recall that when v(t) s 0, the particle moves to the left, and when v(t) 2 0, the particle moves to the right. Therefore, to calculate the total distance traveled, we must integrate the absolute value of velocity, Iv(t)l. First, find the values of t such that v(t) s o. v(t) so 9t - 4 S0 Therefore, Iv(t)I = -v(t) when v(t) is negative, which within the given time interval is 0 sts Similarly, Iv(t)| = v(t) when v(t) is positive, which within the given time interval is ses 3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Next, we must find the total distance traveled by the particle in the given time interval. This is different than displacement, which only measures the difference between the beginning and end points. There may be positive distance and negative distance
traveled that cancel each other out in the net change.
Recall that when v(t) < 0, the particle moves to the left, and when v(t) 2 0, the particle moves to the right. Therefore, to calculate the total distance traveled, we must integrate the absolute value of velocity, Iv(t)|.
First, find the values of t such that v(t) < 0.
v(t) s o
9t - 4 s 0
ts
Therefore, Iv(t)| = -v(t) when v(t) is negative, which within the given time interval is 0 sts
Similarly, Iv(t)| = v(t) when v(t) is positive, which within the given time interval is
sts 3.
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