Motion In A Plane

Question

The x and y coordinates of a particle moving in a plane are given be x(t) = acos(pt) and y(t) = bsin(pt) where a, b (<a) and p are positive constants of appropriate dimensions and t is time. Then , which of the following is not true?

The path of the particle is an ellipse

Velocity and acceleration of the particle are perpendicular to each other at t = π/2p

Acceleration of the particle is always directed towards a fixed point

Distance travelled by the particle in the time interval between t = 0 and t = π/2p is a

Solution

Distance travelled by the particle in the time interval between t = 0 and t = π/2p is a

x = a cos (pt), y =b sin (pt)

$∴ \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, i . e . equation of ellipse Now, r = x \hat{i} + y \hat{j} = a \cos (pt) \hat{i} + b \sin (pt) \hat{j} v = \frac{dr}{dt} = - pasin (pt) \hat{i} + pb \cos (pt) \hat{j} a = \frac{dv}{dt} = - p^{2} a \cos (pt) \hat{i} - p^{2} b \sin (pt) \hat{j} at t = \frac{π}{2 p} v = - pa \hat{i} and a = - p^{2} b \hat{j} v ⊥ a$

also, a = - p²r, i.e directed towards a fixed point.

Some More Questions From Motion in A Plane Chapter

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.

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

Give two examples of polar vectors.

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.