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acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units
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acceleration of a body varies with displacement according to law a=2x....
Solution:
Given, acceleration of a body varies with displacement according to law a=2x.
Let's find the velocity of the body at x=5.
We know that, acceleration a = dv/dt, where v is the velocity of the body and t is time.
Integrating both sides, we get,
∫a dx = ∫dv/dt dx
2∫xdx = ∫dv
v = 2x^2/2 + C1
Given, the velocity is 0 at x=1.
Therefore, 0 = 2(1)^2/2 + C1
C1 = -1
Hence, the velocity of the body at x=5 is,
v = 2(5)^2/2 - 1 = 24 units (approximately)
Therefore, the correct option is (b) 8 units.
Explanation:
To solve the problem, we have used the basic kinematic equation that relates acceleration, velocity, and displacement. We have integrated both sides of the equation to get the velocity of the body at x=5. We have also used the initial condition that the velocity is 0 at x=1 to determine the constant of integration. Finally, we have substituted the value of x=5 to obtain the velocity of the body.
Given, acceleration of a body varies with displacement according to law a=2x.
Let's find the velocity of the body at x=5.
We know that, acceleration a = dv/dt, where v is the velocity of the body and t is time.
Integrating both sides, we get,
∫a dx = ∫dv/dt dx
2∫xdx = ∫dv
v = 2x^2/2 + C1
Given, the velocity is 0 at x=1.
Therefore, 0 = 2(1)^2/2 + C1
C1 = -1
Hence, the velocity of the body at x=5 is,
v = 2(5)^2/2 - 1 = 24 units (approximately)
Therefore, the correct option is (b) 8 units.
Explanation:
To solve the problem, we have used the basic kinematic equation that relates acceleration, velocity, and displacement. We have integrated both sides of the equation to get the velocity of the body at x=5. We have also used the initial condition that the velocity is 0 at x=1 to determine the constant of integration. Finally, we have substituted the value of x=5 to obtain the velocity of the body.
Community Answer
acceleration of a body varies with displacement according to law a=2x....
A=v*dv/dx
vdv=2xdx
now we can integrate & apply limit from x=1 to x=5
vdv=2xdx
now we can integrate & apply limit from x=1 to x=5
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acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units
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acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units.
acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for acceleration of a body varies with displacement according to law a=2x. Given velocity is 0 at x=1 the velocity at x=5 is approximatelya)7 unitsb)8 unitsc)5 unitsd)6 units.
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