NEET Exam > NEET Questions > A particle moves a distance 'x' in time 't' a...
Start Learning for Free
A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer!
Most Upvoted Answer
A particle moves a distance 'x' in time 't' according to equation x=(t...
Acceleration is the rate of change of velocity with respect to time. In order to determine the acceleration of the particle, we need to find the velocity function first.
1. Finding the velocity function:
We are given the equation for the distance traveled by the particle, x=(t^5)^-1. To find the velocity function, we need to differentiate x with respect to time (t).
Taking the derivative of x with respect to t, we can use the chain rule:
dx/dt = d/dt((t^5)^-1)
= -1(t^5)^-2 * d/dt(t^5)
= -1(t^5)^-2 * 5t^4
= -5t^4/(t^5)^2
= -5t^4/t^10
= -5/t^6
Therefore, the velocity function v(t) = dx/dt = -5/t^6.
2. Finding the acceleration function:
To find the acceleration function, we need to differentiate the velocity function with respect to time (t).
Taking the derivative of v(t) with respect to t:
dv/dt = d/dt(-5/t^6)
= 5(6/t^7)
= 30/t^7
Therefore, the acceleration function a(t) = dv/dt = 30/t^7.
3. Determining the relationship between acceleration and velocity:
Now, let's examine the relationship between acceleration and velocity. We have the velocity function v(t) = -5/t^6 and the acceleration function a(t) = 30/t^7.
Let's substitute the velocity function into the acceleration function:
a(t) = 30/t^7
= 30/((-5/t^6)^7)
= 30/((-5)^7/t^(6*7))
= 30/((-5)^7/t^42)
= 30/(5^7/t^42)
= (30*t^42)/(5^7)
From the above equation, we can see that the acceleration is proportional to (velocity)^3/2. Therefore, the correct option is 1.) (velocity)^3/2.
1. Finding the velocity function:
We are given the equation for the distance traveled by the particle, x=(t^5)^-1. To find the velocity function, we need to differentiate x with respect to time (t).
Taking the derivative of x with respect to t, we can use the chain rule:
dx/dt = d/dt((t^5)^-1)
= -1(t^5)^-2 * d/dt(t^5)
= -1(t^5)^-2 * 5t^4
= -5t^4/(t^5)^2
= -5t^4/t^10
= -5/t^6
Therefore, the velocity function v(t) = dx/dt = -5/t^6.
2. Finding the acceleration function:
To find the acceleration function, we need to differentiate the velocity function with respect to time (t).
Taking the derivative of v(t) with respect to t:
dv/dt = d/dt(-5/t^6)
= 5(6/t^7)
= 30/t^7
Therefore, the acceleration function a(t) = dv/dt = 30/t^7.
3. Determining the relationship between acceleration and velocity:
Now, let's examine the relationship between acceleration and velocity. We have the velocity function v(t) = -5/t^6 and the acceleration function a(t) = 30/t^7.
Let's substitute the velocity function into the acceleration function:
a(t) = 30/t^7
= 30/((-5/t^6)^7)
= 30/((-5)^7/t^(6*7))
= 30/((-5)^7/t^42)
= 30/(5^7/t^42)
= (30*t^42)/(5^7)
From the above equation, we can see that the acceleration is proportional to (velocity)^3/2. Therefore, the correct option is 1.) (velocity)^3/2.
Community Answer
A particle moves a distance 'x' in time 't' according to equation x=(t...
x=( t+5)^-1 . v= dx/dt = -- ( t+5)^ -2. tht means (t+5)= --v ^ -1/2 . now, a= dv/dt = 2 ( t+5) ^ -3. , a= 2( - v ^ -1/2) ^ -3, a = -- 2 v ^ 3/2, tht is a is prop to vel ^3/2
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 moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer!
Question Description
A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! 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 moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer!.
A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! 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 moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer!.
Solutions for A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the 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 A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! defined & explained in the simplest way possible. Besides giving the explanation of
A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer!, a detailed solution for A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! has been provided alongside types of A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! theory, EduRev gives you an
ample number of questions to practice A particle moves a distance 'x' in time 't' according to equation x=(t+5)^-1 . The acceleration of the particle is propotional to ~ 1.) (velocity)^3/2 2.) (distance)^2 3.) (distance)^-2 4.) (velocity)^2/3 the answer is option 1 . please your justify the answer! 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