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The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t2 + 2t. If v is the velocity and a is the acceleration of the particle in consistent units, the motion started with
[2005]
  • a)
    v = 0, a = 0
  • b)
    v = 0, a = 2
  • c)
    v = 2, a = 0
  • d)
    v = 2, a = 2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The time variation of the position of a particle in rectilinear motion...
Given x= 2t3 + t2 + 2t
Velocity : v = dx/dt = 6t2 + 2t + 2
At the start of motion, t = o
V = 0 + 0 + 2
V = 2 m/s
Acceleration; a = dv/dt = 12t + 2
at t = 0
a = 0 + 2
∴ a = 2 m/s2
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Most Upvoted Answer
The time variation of the position of a particle in rectilinear motion...
Given:
The time variation of the position of a particle in rectilinear motion is given by x = 2t^3 + t^2 + 2t.

To find:
The initial velocity (v) and the initial acceleration (a) of the particle.

Solution:
The velocity (v) of a particle is the derivative of its position with respect to time, and the acceleration (a) is the derivative of velocity with respect to time.

Step 1: Differentiate the given position equation with respect to time to find the velocity equation.
dx/dt = 6t^2 + 2t + 2

Step 2: Simplify the velocity equation.
v = 6t^2 + 2t + 2

Step 3: Substitute t = 0 in the velocity equation to find the initial velocity.
At t = 0,
v = 6(0)^2 + 2(0) + 2
v = 0 + 0 + 2
v = 2

Therefore, the initial velocity of the particle is v = 2.

Step 4: Differentiate the velocity equation with respect to time to find the acceleration equation.
dv/dt = 12t + 2

Step 5: Simplify the acceleration equation.
a = 12t + 2

Step 6: Substitute t = 0 in the acceleration equation to find the initial acceleration.
At t = 0,
a = 12(0) + 2
a = 0 + 2
a = 2

Therefore, the initial acceleration of the particle is a = 2.

Conclusion:
The motion started with v = 2 and a = 2. Therefore, the correct answer is option D.
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The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t2 + 2t. If v is the velocity and a is the acceleration of the particle in consistent units, the motion started with[2005]a)v = 0, a = 0b)v = 0, a = 2c)v = 2, a = 0d)v = 2, a = 2Correct answer is option 'D'. Can you explain this answer?
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The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t2 + 2t. If v is the velocity and a is the acceleration of the particle in consistent units, the motion started with[2005]a)v = 0, a = 0b)v = 0, a = 2c)v = 2, a = 0d)v = 2, a = 2Correct answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t2 + 2t. If v is the velocity and a is the acceleration of the particle in consistent units, the motion started with[2005]a)v = 0, a = 0b)v = 0, a = 2c)v = 2, a = 0d)v = 2, a = 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t2 + 2t. If v is the velocity and a is the acceleration of the particle in consistent units, the motion started with[2005]a)v = 0, a = 0b)v = 0, a = 2c)v = 2, a = 0d)v = 2, a = 2Correct answer is option 'D'. Can you explain this answer?.
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