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A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be?
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A particle is moving in straight line with initial velocity u and unif...
Understanding the Problem
To find the velocity of a particle moving in a straight line with an initial velocity (u) and uniform acceleration (a), we need to analyze the information given regarding the distances covered during specific seconds.
Distance in the nth Second
The distance traveled by the particle in the nth second can be calculated using the formula:
Distance in nth second = u + a(n - 0.5)
For the 10th second (n=10):
- Distance in 10th second = u + a(10 - 0.5) = u + 9.5a
For the 11th second (n=11):
- Distance in 11th second = u + a(11 - 0.5) = u + 10.5a
Total Distance Covered
According to the problem, the sum of the distances covered in the 10th and 11th seconds is 80m:
(u + 9.5a) + (u + 10.5a) = 80
This simplifies to:
2u + 20a = 80
So, we can deduce:
u + 10a = 40 (Equation 1)
Finding Velocity After 10 Seconds
The velocity of the particle after t seconds is given by:
Velocity (v) = u + at
For t = 10 seconds:
v = u + 10a
Now, substituting from Equation 1:
- We know u + 10a = 40
Thus, the velocity of the particle after 10 seconds is:
Final Answer
v = 40 m/s
This represents the particle's velocity after 10 seconds of uniform acceleration.
To find the velocity of a particle moving in a straight line with an initial velocity (u) and uniform acceleration (a), we need to analyze the information given regarding the distances covered during specific seconds.
Distance in the nth Second
The distance traveled by the particle in the nth second can be calculated using the formula:
Distance in nth second = u + a(n - 0.5)
For the 10th second (n=10):
- Distance in 10th second = u + a(10 - 0.5) = u + 9.5a
For the 11th second (n=11):
- Distance in 11th second = u + a(11 - 0.5) = u + 10.5a
Total Distance Covered
According to the problem, the sum of the distances covered in the 10th and 11th seconds is 80m:
(u + 9.5a) + (u + 10.5a) = 80
This simplifies to:
2u + 20a = 80
So, we can deduce:
u + 10a = 40 (Equation 1)
Finding Velocity After 10 Seconds
The velocity of the particle after t seconds is given by:
Velocity (v) = u + at
For t = 10 seconds:
v = u + 10a
Now, substituting from Equation 1:
- We know u + 10a = 40
Thus, the velocity of the particle after 10 seconds is:
Final Answer
v = 40 m/s
This represents the particle's velocity after 10 seconds of uniform acceleration.
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A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be?
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A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be?.
A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in straight line with initial velocity u and uniform acceleration a. if sumof the 10th second and 11th second is 80m the velocity of particle after 10 seconds will be?.
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