Class 12 Exam > Class 12 Questions > A particle starts from the origin with a velo...
Start Learning for Free
A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?
- a)27cm/sec
- b)28 cm/sec
- c)29 cm/sec
- d)30 cm/sec
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A particle starts from the origin with a velocity 5cm/sec and moves in...
Let x cm be the distance of the moving particle from the origin and v cm/sec be its velocity at the end of t seconds. Then the acceleration of the particle at time t seconds = dv/dt and its velocity at that time = v = dx/dt.
By question, dv/dt = 3t2 – 5t
Or, dv = 3t2 dt – 5tdt
Or, ∫dv = 3∫t2 dt – 5∫t dt
Or, v = t3 – (5/2)t2 + c ……….(1)
Given, v = 5, when t = 0; hence putting these values in equation (1) we get, c = 5
Thus v = t3 – (5/2)t2 + 5
Or, dx/dt = t3 – (5/2)t2 + 5 ………..(2)
Thus, the velocity of the particle at the end of 4 seconds,
= [v]t = 4 = (43 – (5/2)42 + 5 ) cm/sec [putting t = 4 in (2)]
= 29 cm/sec
By question, dv/dt = 3t2 – 5t
Or, dv = 3t2 dt – 5tdt
Or, ∫dv = 3∫t2 dt – 5∫t dt
Or, v = t3 – (5/2)t2 + c ……….(1)
Given, v = 5, when t = 0; hence putting these values in equation (1) we get, c = 5
Thus v = t3 – (5/2)t2 + 5
Or, dx/dt = t3 – (5/2)t2 + 5 ………..(2)
Thus, the velocity of the particle at the end of 4 seconds,
= [v]t = 4 = (43 – (5/2)42 + 5 ) cm/sec [putting t = 4 in (2)]
= 29 cm/sec
Free Test
FREE
| Start Free Test |
Community Answer
A particle starts from the origin with a velocity 5cm/sec and moves in...
To find the equation of motion for the particle, we need to integrate the acceleration function.
Given:
Velocity (v) = 5 cm/sec
Acceleration (a) = 3t^2 cm/sec^2
Integrating acceleration gives us velocity:
v = ∫(3t^2) dt
v = t^3 + C1
Given that the initial velocity is 5 cm/sec, we can substitute this value into the equation:
5 = (0^3) + C1
C1 = 5
So, the equation for velocity is:
v = t^3 + 5
Now, to find the equation for displacement, we need to integrate velocity:
s = ∫(t^3 + 5) dt
s = (1/4)t^4 + 5t + C2
Since the particle starts from the origin (s = 0 at t = 0), we can substitute these values into the equation:
0 = (1/4)(0^4) + 5(0) + C2
C2 = 0
Therefore, the equation for displacement is:
s = (1/4)t^4 + 5t
Given:
Velocity (v) = 5 cm/sec
Acceleration (a) = 3t^2 cm/sec^2
Integrating acceleration gives us velocity:
v = ∫(3t^2) dt
v = t^3 + C1
Given that the initial velocity is 5 cm/sec, we can substitute this value into the equation:
5 = (0^3) + C1
C1 = 5
So, the equation for velocity is:
v = t^3 + 5
Now, to find the equation for displacement, we need to integrate velocity:
s = ∫(t^3 + 5) dt
s = (1/4)t^4 + 5t + C2
Since the particle starts from the origin (s = 0 at t = 0), we can substitute these values into the equation:
0 = (1/4)(0^4) + 5(0) + C2
C2 = 0
Therefore, the equation for displacement is:
s = (1/4)t^4 + 5t
|
Explore Courses for Class 12 exam
|
|
A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer?
Question Description
A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer?.
A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12.
Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
Here you can find the meaning of A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A particle starts from the origin with a velocity 5cm/sec and moves in a straight line, its acceleration at time t seconds being (3t2 – 5t)cm/sec2. What will be the velocity of the particle?a)27cm/secb)28 cm/secc)29 cm/secd)30 cm/secCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 12 tests.
|
|
Explore Courses for Class 12 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
|
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