JEE Exam > JEE Questions > The acceleration of a particle increases line...
Start Learning for Free
The acceleration of a particle increases linearly with time t as 6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in time t will be
- a)t
- b)t2
- c)t3
- d)t4
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The acceleration of a particle increases linearly with timet as6t. If ...
Explanation:
Given:
- Acceleration of the particle: a(t) = 6t
- Initial velocity of the particle: 0
- Particle starts from the origin
Using kinematic equations:
- We know that acceleration is the derivative of velocity with respect to time, which means:
a(t) = dv/dt
- Integrating both sides with respect to time, we get:
∫a(t) dt = ∫dv
- Integrating the given acceleration function, we get:
∫6t dt = v
v = 3t^2
- Since the initial velocity is 0, we have v(0) = 0, which means the velocity function is:
v(t) = 3t^2
- Distance travelled by the particle is the integral of velocity with respect to time:
∫v(t) dt = ∫3t^2 dt
∫3t^2 dt = t^3
Therefore, the distance travelled by the particle in time t is t^3, which corresponds to option 'c'.
Given:
- Acceleration of the particle: a(t) = 6t
- Initial velocity of the particle: 0
- Particle starts from the origin
Using kinematic equations:
- We know that acceleration is the derivative of velocity with respect to time, which means:
a(t) = dv/dt
- Integrating both sides with respect to time, we get:
∫a(t) dt = ∫dv
- Integrating the given acceleration function, we get:
∫6t dt = v
v = 3t^2
- Since the initial velocity is 0, we have v(0) = 0, which means the velocity function is:
v(t) = 3t^2
- Distance travelled by the particle is the integral of velocity with respect to time:
∫v(t) dt = ∫3t^2 dt
∫3t^2 dt = t^3
Therefore, the distance travelled by the particle in time t is t^3, which corresponds to option 'c'.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer?
Question Description
The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer?.
The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer?.
Solutions for The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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