A particle of unit mass undergoes one-dimensional motion such that its velocity according to
V(x) = βx^-2n where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by

-2nβ² x^-2n-1

-2nβ²x^-4n-1

-2β x^-2n+1

-2nβ²e^-4n+1

Solution

-2nβ²x^-4n-1

Given, v = βx^-2n
$straight a equals space dv over dt equals dx over dt. dv over dx straight a equals straight v dv over dx equals left parenthesis space βx to the power of negative 2 straight n end exponent right parenthesis left parenthesis negative 2 straight n space βx to the power of negative 2 straight n minus 1 end exponent right parenthesis straight a equals negative 2 nβ squared straight x to the power of negative 4 straight n minus 1 end exponent$

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

A particle of unit mass undergoes one-dimensional motion such that its velocity according toV(x) = βx-2n where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by -2nβ2 x-2n-1 -2nβ2 x-4n-1 -2β x-2n+1 -2nβ2e-4n+1

Some More Questions From Motion in A Plane Chapter

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.