A particle moves a distance x in time t according to equation x = (t +5)^-1. The acceleration of particle is proportional to

(velocity)^3/2

(distance)²

(distance)^-2

(velocity)^2/3

Solution

(velocity)^3/2

Given, distance x = ( t + 5)^-1 ...... (i)
Differentiating eq. (i) w.r.t, we get
$dx over dt space equals space straight v space equals space fraction numerator negative 1 over denominator left parenthesis straight t plus 5 right parenthesis squared end fraction space space space space.... space left parenthesis ii right parenthesis Again space comma space differentiating space eq space left parenthesis straight i right parenthesis thin space straight w. straight r. straight t comma space we space get fraction numerator straight d squared straight x over denominator dt squared end fraction space equals space left parenthesis straight a right parenthesis space equals space fraction numerator 2 over denominator left parenthesis straight t space plus 5 right parenthesis cubed end fraction Comparing space eqs. space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get left parenthesis straight a right parenthesis space proportional to space left parenthesis straight v right parenthesis to the power of 3 divided by 2 end exponent$

Some More Questions From Motion in A Plane Chapter

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 moves a distance x in time t according to equation x = (t +5)^-1. The acceleration of particle is proportional to

(velocity)^3/2

(distance)²

(distance)^-2

(velocity)^2/3

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Motion In A Plane

A particle moves a distance x in time t according to equation x = (t +5)-1. The acceleration of particle is proportional to (velocity)3/2 (distance)2 (distance)-2 (velocity)2/3

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A particle moves a distance x in time t according to equation x = (t +5)^-1. The acceleration of particle is proportional to

(velocity)^3/2

(distance)²

(distance)^-2

(velocity)^2/3

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.