NEET Exam > NEET Questions > The acceleration 'a' in m/s² of a particle is...
Start Learning for Free
The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be?
Most Upvoted Answer
The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 whe...
Explanation:
Given, acceleration (a) = 3t^2 + 2t + 2 m/s²
Initial velocity (u) = 2 m/s
Time (t) = 2 s
We need to find the final velocity (v) of the particle after 2 seconds.
Step 1: Finding the velocity of the particle at any time (t)
We know that acceleration (a) is the rate of change of velocity (v) with respect to time (t).
So, integrating the acceleration with respect to time, we get velocity (v) at any time (t).
v = ∫a dt = ∫(3t^2 + 2t + 2) dt = t^3 + t^2 + 2t + C
where C is the constant of integration.
Step 2: Finding the constant of integration (C)
We can find the value of C using the initial velocity (u).
At t = 0, v = u
So, u = 0^3 + 0^2 + 2(0) + C = C
Therefore, C = 2 m/s.
Step 3: Finding the final velocity (v) after 2 seconds
Now, putting the values of C and t in the equation of velocity, we get
v = t^3 + t^2 + 2t + 2 m/s
At t = 2 s,
v = 2^3 + 2^2 + 2(2) + 2 = 18 m/s
Therefore, the final velocity (v) of the particle after 2 seconds is 18 m/s.
Given, acceleration (a) = 3t^2 + 2t + 2 m/s²
Initial velocity (u) = 2 m/s
Time (t) = 2 s
We need to find the final velocity (v) of the particle after 2 seconds.
Step 1: Finding the velocity of the particle at any time (t)
We know that acceleration (a) is the rate of change of velocity (v) with respect to time (t).
So, integrating the acceleration with respect to time, we get velocity (v) at any time (t).
v = ∫a dt = ∫(3t^2 + 2t + 2) dt = t^3 + t^2 + 2t + C
where C is the constant of integration.
Step 2: Finding the constant of integration (C)
We can find the value of C using the initial velocity (u).
At t = 0, v = u
So, u = 0^3 + 0^2 + 2(0) + C = C
Therefore, C = 2 m/s.
Step 3: Finding the final velocity (v) after 2 seconds
Now, putting the values of C and t in the equation of velocity, we get
v = t^3 + t^2 + 2t + 2 m/s
At t = 2 s,
v = 2^3 + 2^2 + 2(2) + 2 = 18 m/s
Therefore, the final velocity (v) of the particle after 2 seconds is 18 m/s.
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
The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be?
Question Description
The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be?.
The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be?.
Solutions for The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? 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 acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? defined & explained in the simplest way possible. Besides giving the explanation of
The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be?, a detailed solution for The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? has been provided alongside types of The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? theory, EduRev gives you an
ample number of questions to practice The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be? 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup