Question

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as

t³

t²

t

t^1/2

Solution

t²

straight v equals space straight alpha square root of straight x dx over dt space equals space straight alpha square root of straight x space space space space open parentheses therefore space straight v space equals space dv over dt close parentheses fraction numerator dx over denominator square root of straight x end fraction space equals space straight alpha space dt Perform space integration integral subscript 0 superscript straight x fraction numerator dx over denominator square root of straight x end fraction space equals space integral subscript 0 superscript straight t straight alpha space dt because space at space straight t space equals space 0 comma space straight x space equals space 0 space and space let space at space any space time space straight t comma space particle space is space at space straight x right square bracket rightwards double arrow right enclose space fraction numerator straight x to the power of 1 divided by 2 end exponent over denominator 1 divided by 2 end fraction end enclose subscript 0 superscript straight x space equals space αt rightwards double arrow space straight x to the power of 1 divided by 2 end exponent space equals space straight alpha over 2 straight t rightwards double arrow space straight x space equals space straight alpha squared over 4 straight x space straight t squared space rightwards double arrow space straight x proportional to space straight t squared

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

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

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as

t³

t²

t

t^1/2

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as t3 t2 t t1/2

Some More Questions From Motion in A Plane Chapter

Is a physical quantity, having a direction, necessarily a vector?

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity ‘v’ that varies as v= α√x . The displacement of the particle varies with time as

t³

t²

t

t^1/2

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.