NEET Exam > NEET Questions > The motion of a particle is described by x = ...
Start Learning for Free
The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0 > 0, k > 0. With what velocity does the particle start?
- a)x0/k
- b)x0k
- c)k/x0
- d)2x0k
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The motion of a particle is described by x = x0(1 − e−kt);...
Free Test
FREE
| Start Free Test |
Community Answer
The motion of a particle is described by x = x0(1 − e−kt);...
+ cos(ωt)), where x0 is the amplitude of the motion and ω is the angular frequency.
To find the period of the motion, we can use the formula T = 2π/ω, where T is the period.
We know that the argument of the cosine function must be in radians, so we need to convert the frequency from cycles per second to radians per second. This can be done using the formula ω = 2πf, where f is the frequency in cycles per second.
Substituting the given expression for x into the formula for ω, we get:
ω = 2πf = 2π/T
f = (1/T)
x = x0(1 + cos(ωt))
Differentiating x with respect to time gives:
v = dx/dt = -x0ωsin(ωt)
Differentiating v with respect to time gives:
a = dv/dt = -x0ω^2cos(ωt)
At t = 0, x = x0(1 + cos(0)) = 2x0
v = -x0ωsin(0) = 0
a = -x0ω^2cos(0) = -x0ω^2
Therefore, the period of the motion is:
T = 2π/ω = 2π/(2π/T) = T
So the period of the motion is T.
To find the period of the motion, we can use the formula T = 2π/ω, where T is the period.
We know that the argument of the cosine function must be in radians, so we need to convert the frequency from cycles per second to radians per second. This can be done using the formula ω = 2πf, where f is the frequency in cycles per second.
Substituting the given expression for x into the formula for ω, we get:
ω = 2πf = 2π/T
f = (1/T)
x = x0(1 + cos(ωt))
Differentiating x with respect to time gives:
v = dx/dt = -x0ωsin(ωt)
Differentiating v with respect to time gives:
a = dv/dt = -x0ω^2cos(ωt)
At t = 0, x = x0(1 + cos(0)) = 2x0
v = -x0ωsin(0) = 0
a = -x0ω^2cos(0) = -x0ω^2
Therefore, the period of the motion is:
T = 2π/ω = 2π/(2π/T) = T
So the period of the motion is T.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer?
Question Description
The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer?.
The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The motion of a particle is described by x = x0(1 − e−kt); t ≥ 0; x0> 0, k > 0. With what velocity does the particle start?a)x0/kb)x0kc)k/x0d)2x0kCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup