Yahoo Answers: Answers and Comments for Find the open tintervals on which the particle is moving to the right. (Enter your answer using interval notation.)? [Physics]
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From Anonymous
enUS
Tue, 23 Apr 2019 13:16:27 +0000
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Yahoo Answers: Answers and Comments for Find the open tintervals on which the particle is moving to the right. (Enter your answer using interval notation.)? [Physics]
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https://answers.yahoo.com/question/index?qid=20190423131627AAKSo6R
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From electron1: I will assume the unit of distance is meters.
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https://answers.yahoo.com/question/index?qid=20190423131627AAKSo6R
https://answers.yahoo.com/question/index?qid=20190423131627AAKSo6R
Tue, 23 Apr 2019 17:02:12 +0000
I will assume the unit of distance is meters.
x(t) = t^3 – 12 * t^2 + 21 * t – 5
The equation of velocity versus time is the first derivative of this equation.
v(t) = 3 * t^2 – 24 * t + 21
The initial velocity is 21 m/s. The equation of acceleration versus time is the first derivative of this equation.
a(t) = 6 * t – 24
6 * t – 24 = 0
t = 4 seconds.
Let’s use this time in the velocity versus time equation.
v = 3 * 2^2 – 12 * 2 + 21 = 9 m/s
Since the velocity is positive, I assume the particle is moving to the right. The next step is to determine the time when the particle’s velocity is 0 m/s.
3 * t^2 – 24 * t + 21 = 0
t = [24 ± √(576 – 4 * 3 * 21)] ÷ 6
t = [24 ± 18] ÷ 6
t1 = 7 seconds
t2 = 1 second
These are the two times when object’s velocity is 0 m/s. This is all that I know how to do.

From Some Body: x(t) = t³ − 12t² + 21t − 5
Velocity is the fi...
https://answers.yahoo.com/question/index?qid=20190423131627AAKSo6R
https://answers.yahoo.com/question/index?qid=20190423131627AAKSo6R
Tue, 23 Apr 2019 13:26:41 +0000
x(t) = t³ − 12t² + 21t − 5
Velocity is the first derivative:
v(t) = 3t² − 24t + 21
Acceleration is the second derivative:
a(t) = 6t − 24
When acceleration is 0:
0 = 6t − 24
t = 4
Find v(4).
The particle is moving to the right when velocity is positive. First find where velocity is 0:
0 = 3t² − 24t + 21
0 = t² − 8t + 7
0 = (t − 1)(t − 7)
t = 1, 7
Evaluate v(t) on the intervals (0, 1), (1, 7), and (7, 10). Determine which ones are where v(t) is positive.