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A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is?
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A body freely falling from rest has a velocity v after it falls throug...
Distance for Velocity to become Double
To find the distance the body falls down further for its velocity to become double, we need to consider the equations of motion for uniformly accelerated motion.
Initial Velocity:
When the body is freely falling from rest, its initial velocity (u) is 0 m/s.
Final Velocity:
Let the final velocity of the body after falling through a distance h be v m/s.
First Equation of Motion:
v² = u² + 2as
where v is final velocity, u is initial velocity, a is acceleration, and s is displacement.
Second Equation of Motion:
v = u + at
where v is final velocity, u is initial velocity, a is acceleration, t is time.
Third Equation of Motion:
s = ut + (1/2)at²
where s is displacement, u is initial velocity, a is acceleration, and t is time.
Given:
v = 2u (velocity becomes double)
Using the first equation of motion:
(2u)² = 0 + 2as
4u² = 2as
2u² = as
Calculating Time:
Using the second equation of motion:
2u = 0 + at
t = 2u/a
t = 2u/g (as acceleration due to gravity is g)
Distance for Velocity to become Double:
Using the third equation of motion:
s = 0 + (1/2)g(2u/g)²
s = (1/2) * 4u²/g
s = 2u²/g
Therefore, the distance the body falls down further for its velocity to become double is 2u²/g.
To find the distance the body falls down further for its velocity to become double, we need to consider the equations of motion for uniformly accelerated motion.
Initial Velocity:
When the body is freely falling from rest, its initial velocity (u) is 0 m/s.
Final Velocity:
Let the final velocity of the body after falling through a distance h be v m/s.
First Equation of Motion:
v² = u² + 2as
where v is final velocity, u is initial velocity, a is acceleration, and s is displacement.
Second Equation of Motion:
v = u + at
where v is final velocity, u is initial velocity, a is acceleration, t is time.
Third Equation of Motion:
s = ut + (1/2)at²
where s is displacement, u is initial velocity, a is acceleration, and t is time.
Given:
v = 2u (velocity becomes double)
Using the first equation of motion:
(2u)² = 0 + 2as
4u² = 2as
2u² = as
Calculating Time:
Using the second equation of motion:
2u = 0 + at
t = 2u/a
t = 2u/g (as acceleration due to gravity is g)
Distance for Velocity to become Double:
Using the third equation of motion:
s = 0 + (1/2)g(2u/g)²
s = (1/2) * 4u²/g
s = 2u²/g
Therefore, the distance the body falls down further for its velocity to become double is 2u²/g.
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A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is?
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A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is?.
A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body freely falling from rest has a velocity v after it falls through a distance h the distance it falls down further for it velocity to become double is?.
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