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A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?
- a)The retardation of the particle is the cube of its velocity
- b)The acceleration of the particle is the cube of its velocity
- c)The retardation of the particle is the square of its velocity
- d)The acceleration of the particle is the square of its velocity
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A particle moving in a straight line traverses a distance x in time t....
Explanation:
Given,
Distance travelled, x = x
Time taken, t = x2/2x
To find the acceleration and retardation of the particle, we need to differentiate the distance equation with respect to time.
Differentiating x with respect to time, we get the velocity equation, v.
Differentiating v with respect to time, we get the acceleration equation, a.
Differentiating a with respect to time, we get the retardation equation, r.
Finding Velocity:
We know that,
v = dx/dt
Differentiating x with respect to time, we get
v = x/t
Substituting the value of t from the given equation, we get
v = 2x/x2
v = 2/x
Finding Acceleration:
We know that,
a = dv/dt
Differentiating v with respect to time, we get
a = -2/x2
Finding Retardation:
We know that,
r = da/dt
Differentiating a with respect to time, we get
r = 4/x3
Comparing the options with the derived equations, we can see that Option A is correct.
Therefore, the retardation of the particle is the cube of its velocity.
Given,
Distance travelled, x = x
Time taken, t = x2/2x
To find the acceleration and retardation of the particle, we need to differentiate the distance equation with respect to time.
Differentiating x with respect to time, we get the velocity equation, v.
Differentiating v with respect to time, we get the acceleration equation, a.
Differentiating a with respect to time, we get the retardation equation, r.
Finding Velocity:
We know that,
v = dx/dt
Differentiating x with respect to time, we get
v = x/t
Substituting the value of t from the given equation, we get
v = 2x/x2
v = 2/x
Finding Acceleration:
We know that,
a = dv/dt
Differentiating v with respect to time, we get
a = -2/x2
Finding Retardation:
We know that,
r = da/dt
Differentiating a with respect to time, we get
r = 4/x3
Comparing the options with the derived equations, we can see that Option A is correct.
Therefore, the retardation of the particle is the cube of its velocity.
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Community Answer
A particle moving in a straight line traverses a distance x in time t....
We have, t = x2/2 + x
Therefore, dt/dx = 2x/2 + 1 = x + 1
Thus, if v be the velocity of the particle at time t, then
v = dx/dt = 1/(dt/dx)
= 1/(x + 1) = (x + 1)-1
Thus dv/dt = d((x + 1)-1)/dt
= (-1)(x + 1)-2 d(x + 1)/dt
= -1/(x + 1)2 * dx/dt
As, 1/(x + 1) = dx/dt,
So, -(dx/dt)2(dx/dt)
Or dv/dt = -v2*v [as, dx/dt = v]
= -v3
We know, dv/dt = acceleration of a particle.
As, dv/dt is negative, so there is a retardation of the particle.
Thus, the retardation of the particle = -dv/dt = v3 = cube of the particle.
Therefore, dt/dx = 2x/2 + 1 = x + 1
Thus, if v be the velocity of the particle at time t, then
v = dx/dt = 1/(dt/dx)
= 1/(x + 1) = (x + 1)-1
Thus dv/dt = d((x + 1)-1)/dt
= (-1)(x + 1)-2 d(x + 1)/dt
= -1/(x + 1)2 * dx/dt
As, 1/(x + 1) = dx/dt,
So, -(dx/dt)2(dx/dt)
Or dv/dt = -v2*v [as, dx/dt = v]
= -v3
We know, dv/dt = acceleration of a particle.
As, dv/dt is negative, so there is a retardation of the particle.
Thus, the retardation of the particle = -dv/dt = v3 = cube of the particle.
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A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?a)The retardation of the particle is the cube of its velocityb)The acceleration of the particle is the cube of its velocityc)The retardation of the particle is the square of its velocityd)The acceleration of the particle is the square of its velocityCorrect answer is option 'A'. Can you explain this answer?
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A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?a)The retardation of the particle is the cube of its velocityb)The acceleration of the particle is the cube of its velocityc)The retardation of the particle is the square of its velocityd)The acceleration of the particle is the square of its velocityCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?a)The retardation of the particle is the cube of its velocityb)The acceleration of the particle is the cube of its velocityc)The retardation of the particle is the square of its velocityd)The acceleration of the particle is the square of its velocityCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?a)The retardation of the particle is the cube of its velocityb)The acceleration of the particle is the cube of its velocityc)The retardation of the particle is the square of its velocityd)The acceleration of the particle is the square of its velocityCorrect answer is option 'A'. Can you explain this answer?.
A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?a)The retardation of the particle is the cube of its velocityb)The acceleration of the particle is the cube of its velocityc)The retardation of the particle is the square of its velocityd)The acceleration of the particle is the square of its velocityCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?a)The retardation of the particle is the cube of its velocityb)The acceleration of the particle is the cube of its velocityc)The retardation of the particle is the square of its velocityd)The acceleration of the particle is the square of its velocityCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moving in a straight line traverses a distance x in time t. If t = x2/2 + x, then which one is correct?a)The retardation of the particle is the cube of its velocityb)The acceleration of the particle is the cube of its velocityc)The retardation of the particle is the square of its velocityd)The acceleration of the particle is the square of its velocityCorrect answer is option 'A'. Can you explain this answer?.
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