NEET Exam > NEET Questions > A particle is moving in a straight line such ...
Start Learning for Free
A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2?
Most Upvoted Answer
A particle is moving in a straight line such that its velocity varies ...
Introduction:
In this problem, we are given the velocity of a particle as a function of time. We need to find the average velocity of the particle during the time interval in which the velocity decreases from v0 to v0/2.
Derivation:
The velocity of the particle is given by v = v0 e^-λt
Let's find the time taken for the velocity to decrease from v0 to v0/2.
v = v0/2
v0 e^-λt = v0/2
e^-λt = 1/2
-λt = ln(1/2)
-λt = -ln2
t = ln2/λ
Now, we need to find the average velocity of the particle during the time interval from t=0 to t=ln2/λ.
Solution:
Step 1: Find the displacement of the particle during the time interval from t=0 to t=ln2/λ.
The displacement of the particle during this time interval is given by:
Δx = ∫v0/2v0 v(t) dt
= ∫v0/2v0 v0 e^-λt dt
= -v0/λ [e^-λt]v0/2v0
= -v0/λ [e^-(λln2/λ) - 1]
= -v0/λ [1/2 - 1]
= v0/λ [1/2]
Δx = v0/2λ
Step 2: Find the time taken for the particle to travel from v0 to v0/2.
The time taken for the particle to travel from v0 to v0/2 is given by:
t = ln2/λ
Step 3: Find the average velocity of the particle during the time interval from t=0 to t=ln2/λ.
The average velocity of the particle during this time interval is given by:
v_avg = Δx / t
v_avg = (v0/2λ) / (ln2/λ)
v_avg = v0/2 ln2
Conclusion:
Therefore, the average velocity of the particle during the time interval in which the velocity decreases from v0 to v0/2 is v0/2 ln2.
In this problem, we are given the velocity of a particle as a function of time. We need to find the average velocity of the particle during the time interval in which the velocity decreases from v0 to v0/2.
Derivation:
The velocity of the particle is given by v = v0 e^-λt
Let's find the time taken for the velocity to decrease from v0 to v0/2.
v = v0/2
v0 e^-λt = v0/2
e^-λt = 1/2
-λt = ln(1/2)
-λt = -ln2
t = ln2/λ
Now, we need to find the average velocity of the particle during the time interval from t=0 to t=ln2/λ.
Solution:
Step 1: Find the displacement of the particle during the time interval from t=0 to t=ln2/λ.
The displacement of the particle during this time interval is given by:
Δx = ∫v0/2v0 v(t) dt
= ∫v0/2v0 v0 e^-λt dt
= -v0/λ [e^-λt]v0/2v0
= -v0/λ [e^-(λln2/λ) - 1]
= -v0/λ [1/2 - 1]
= v0/λ [1/2]
Δx = v0/2λ
Step 2: Find the time taken for the particle to travel from v0 to v0/2.
The time taken for the particle to travel from v0 to v0/2 is given by:
t = ln2/λ
Step 3: Find the average velocity of the particle during the time interval from t=0 to t=ln2/λ.
The average velocity of the particle during this time interval is given by:
v_avg = Δx / t
v_avg = (v0/2λ) / (ln2/λ)
v_avg = v0/2 ln2
Conclusion:
Therefore, the average velocity of the particle during the time interval in which the velocity decreases from v0 to v0/2 is v0/2 ln2.
Community Answer
A particle is moving in a straight line such that its velocity varies ...
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2?
Question Description
A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2?.
A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2?.
Solutions for A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? 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 A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? defined & explained in the simplest way possible. Besides giving the explanation of
A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2?, a detailed solution for A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? has been provided alongside types of A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? theory, EduRev gives you an
ample number of questions to practice A particle is moving in a straight line such that its velocity varies as v =v0 e-lemda t, where lemda and t are constant. Find the average velocity during the time interval in which the velocity decrease from v0 to v0/2? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup