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A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s?
Verified Answer
A particle starts from rest it, s acceleration at an instant t is a=10...
a = v dv/ds
Now
10 / (v+1) = v dv/ds
Now
10 ds = v (v+1) dv
on integrating
10 s = v^3/3 + v^2/ 2 + c
at v=0
s=0
hence
10 s = v^3/3 + v^2/ 2
now if v = 15 m/sec
10s = 3375/3 + 225/2
10s = 1125 + 112.5
10s = 1237.5
s = 123.75 m
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Most Upvoted Answer
A particle starts from rest it, s acceleration at an instant t is a=10...
Given information:
- Initial velocity (u) = 0 m/s (particle starts from rest)
- Acceleration (a) at an instant t = 10/v1 m/s (where v1 is the instantaneous velocity)
To find:
The distance traveled when the particle attains a velocity of 15 m/s.
Approach:
To solve this problem, we can use the kinematic equation that relates velocity, acceleration, and displacement:
v^2 = u^2 + 2as
Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- s is the displacement
We need to find the displacement s when the velocity v is 15 m/s.
Solution:
Step 1: Find the acceleration at the instant when the velocity is 15 m/s.
Given: a = 10/v1
At v = 15 m/s, substitute the value:
a = 10/15 = 2/3 m/s^2
Step 2: Use the kinematic equation to find the displacement s.
v^2 = u^2 + 2as
Given: u = 0 m/s, a = 2/3 m/s^2, v = 15 m/s
(15)^2 = (0)^2 + 2 * (2/3) * s
225 = 4/3 * s
225 * 3/4 = s
s = 168.75 m
Step 3: Conclusion
The particle will travel a distance of 168.75 meters when it attains a velocity of 15 m/s.
- Initial velocity (u) = 0 m/s (particle starts from rest)
- Acceleration (a) at an instant t = 10/v1 m/s (where v1 is the instantaneous velocity)
To find:
The distance traveled when the particle attains a velocity of 15 m/s.
Approach:
To solve this problem, we can use the kinematic equation that relates velocity, acceleration, and displacement:
v^2 = u^2 + 2as
Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- s is the displacement
We need to find the displacement s when the velocity v is 15 m/s.
Solution:
Step 1: Find the acceleration at the instant when the velocity is 15 m/s.
Given: a = 10/v1
At v = 15 m/s, substitute the value:
a = 10/15 = 2/3 m/s^2
Step 2: Use the kinematic equation to find the displacement s.
v^2 = u^2 + 2as
Given: u = 0 m/s, a = 2/3 m/s^2, v = 15 m/s
(15)^2 = (0)^2 + 2 * (2/3) * s
225 = 4/3 * s
225 * 3/4 = s
s = 168.75 m
Step 3: Conclusion
The particle will travel a distance of 168.75 meters when it attains a velocity of 15 m/s.
Community Answer
A particle starts from rest it, s acceleration at an instant t is a=10...
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A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s?
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A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s?.
A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle starts from rest it, s acceleration at an instant t is a=10/v+1 m/s where v is instantaneous velocity. the distance traveled after which the particle attain a velocity of 15 m/s?.
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