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A particle moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance.
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A particle moves in a straight line with a uniform acceleration 'a' .i...
V=√2as, u=0, then find average speed (v+u)/2 so ..{(√2as)+0} /2=(√as/2)
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A particle moves in a straight line with a uniform acceleration 'a' .i...
Problem: A particle moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. Find the average velocity of the particle in the first 'S' distance.
Solution:
Formula: The average velocity of the particle in the first 'S' distance is given as:
v_avg = (v_f + v_i) / 2
where
v_f = final velocity of the particle
v_i = initial velocity of the particle
S = distance travelled by the particle
Derivation:
We know that the particle is moving with uniform acceleration 'a', so we can use the following formulae:
v_f = u + at ---(1)
S = ut + (1/2)at^2 ---(2)
where
u = initial velocity of the particle
t = time taken by the particle to cover the distance 'S'
From equation (1), we get:
v_f = at ---(3)
Substituting equation (3) in equation (2), we get:
S = (1/2)at^2 ---(4)
From equation (4), we get:
t = sqrt(2S/a) ---(5)
Substituting equation (3) and (5) in the formula for average velocity, we get:
v_avg = (at + 0) / 2
v_avg = (a * sqrt(2S/a)) / 2
Final Answer:
Therefore, the average velocity of the particle in the first 'S' distance is (a * sqrt(2S/a)) / 2.
Solution:
Formula: The average velocity of the particle in the first 'S' distance is given as:
v_avg = (v_f + v_i) / 2
where
v_f = final velocity of the particle
v_i = initial velocity of the particle
S = distance travelled by the particle
Derivation:
We know that the particle is moving with uniform acceleration 'a', so we can use the following formulae:
v_f = u + at ---(1)
S = ut + (1/2)at^2 ---(2)
where
u = initial velocity of the particle
t = time taken by the particle to cover the distance 'S'
From equation (1), we get:
v_f = at ---(3)
Substituting equation (3) in equation (2), we get:
S = (1/2)at^2 ---(4)
From equation (4), we get:
t = sqrt(2S/a) ---(5)
Substituting equation (3) and (5) in the formula for average velocity, we get:
v_avg = (at + 0) / 2
v_avg = (a * sqrt(2S/a)) / 2
Final Answer:
Therefore, the average velocity of the particle in the first 'S' distance is (a * sqrt(2S/a)) / 2.
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A particle moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance.
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A particle moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance. 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 moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance. covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance..
A particle moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance. 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 moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance. covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in a straight line with a uniform acceleration 'a' .initial velocity of the particle is zero. find the average velocity of the particle in first 'S' distance..
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