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The kinetic energy of a body initially at rest is found to be proportional to t^4?
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The kinetic energy of a body initially at rest is found to be proporti...
Explanation:
- Definition of Kinetic Energy: Kinetic energy is the energy of motion of a body. It is directly proportional to the mass of the body and the square of its velocity.
- Initial Velocity: As the body is initially at rest, its initial velocity is zero.
- Proportional to t^4: According to the given statement, the kinetic energy of the body is proportional to t^4.
- Derivation: Let the mass of the body be m and its velocity at time t be v. Then, the kinetic energy of the body can be expressed as:
K.E. = (1/2)mv^2
As the body is initially at rest, v = 0.
Therefore, K.E. = (1/2)m(0)^2 = 0
Now, according to the given statement, the kinetic energy is proportional to t^4.
Therefore, K.E. = kt^4, where k is a constant of proportionality.
Substituting this value of K.E. in the equation (1/2)mv^2, we get:
(1/2)mv^2 = kt^4
v^2 = 2kt^4/m
v = (2kt^4/m)^1/2
Thus, the velocity of the body at time t is proportional to t^2.
Conclusion:
- Hence, we can conclude that the velocity of the body is proportional to t^2 and the kinetic energy is proportional to t^4.
Community Answer
The kinetic energy of a body initially at rest is found to be proporti...
Yes K.E. is proportional to t⁴
Given : u = 0 m/s
let acceleration be constant
We know K.E.= ½mv²
From first law of motion ,we get
v = u + at
v= 0 + at
v= at
Therefore , K.E.=½mv²
=½m(at)²
=½ma²t²
=ma⁴t⁴
Hence ,kinetic energy is proportional to t⁴.
Given : u = 0 m/s
let acceleration be constant
We know K.E.= ½mv²
From first law of motion ,we get
v = u + at
v= 0 + at
v= at
Therefore , K.E.=½mv²
=½m(at)²
=½ma²t²
=ma⁴t⁴
Hence ,kinetic energy is proportional to t⁴.
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The kinetic energy of a body initially at rest is found to be proportional to t^4?
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The kinetic energy of a body initially at rest is found to be proportional to t^4? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The kinetic energy of a body initially at rest is found to be proportional to t^4? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The kinetic energy of a body initially at rest is found to be proportional to t^4?.
The kinetic energy of a body initially at rest is found to be proportional to t^4? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The kinetic energy of a body initially at rest is found to be proportional to t^4? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The kinetic energy of a body initially at rest is found to be proportional to t^4?.
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