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A particle located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2?
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A particle located at x=0 and t=0 and starts moving along positive x-a...
Velocity of the Particle:
- The velocity of the particle is given by v = b√x, where b is a constant and x is the displacement of the particle.
- This means that the velocity of the particle increases as the square root of its displacement.
Displacement of the Particle vs Time:
- The displacement of the particle can be found by integrating the velocity function with respect to time.
- ∫(dx/dt) dt = ∫b√x dt
- dx = b√x dt
- ∫(1/√x) dx = b∫dt
- 2√x = bt + C
- x = (b/2)t^2 + C
Variation of Displacement with Time:
- As we can see from the above equation, the displacement of the particle varies with time as t^2.
- This means that the displacement of the particle is directly proportional to the square of time.
- The option that best represents the variation of displacement with time is t^2.
Therefore, the displacement of the particle varies with time as t^2 when its velocity is given by v = b√x.
- The velocity of the particle is given by v = b√x, where b is a constant and x is the displacement of the particle.
- This means that the velocity of the particle increases as the square root of its displacement.
Displacement of the Particle vs Time:
- The displacement of the particle can be found by integrating the velocity function with respect to time.
- ∫(dx/dt) dt = ∫b√x dt
- dx = b√x dt
- ∫(1/√x) dx = b∫dt
- 2√x = bt + C
- x = (b/2)t^2 + C
Variation of Displacement with Time:
- As we can see from the above equation, the displacement of the particle varies with time as t^2.
- This means that the displacement of the particle is directly proportional to the square of time.
- The option that best represents the variation of displacement with time is t^2.
Therefore, the displacement of the particle varies with time as t^2 when its velocity is given by v = b√x.
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A particle located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2?
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A particle located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2? 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 located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2?.
A particle located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2? 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 located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle located at x=0 and t=0 and starts moving along positive x-axis with a velocity that varies as v=b√x the displacement of particle vary with time as 1)t 2)t^ 3)t1/2 4)t3/2?.
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