Question

The position of a particle is given by

$bold r bold space bold equals bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space straight m$

where t is in seconds and the coefficients have the proper units for r to be in metres.

(a) Find the v and a of the particle?

Solution

straight a right parenthesis thin space straight v with rightwards harpoon with barb upwards on top left parenthesis straight t right parenthesis space equals space left parenthesis 3.0 space straight i with hat on top space minus space 4.0 straight t space straight j with hat on top right parenthesis straight a space equals space minus 4.0 space straight j with hat on top space Position space of space the space particle space is space given space by comma space bold r bold space bold equals bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space straight m Velocity comma space straight v with rightwards harpoon with barb upwards on top equals fraction numerator straight d straight r with rightwards harpoon with barb upwards on top over denominator dt end fraction equals straight d over dt left parenthesis bold space 3.0 space straight t space straight i with hat on top space minus space 2.0 space straight t squared space straight j with hat on top space plus space 4.0 space straight k with hat on top space right parenthesis therefore space straight v with rightwards harpoon with barb upwards on top space equals space 3.0 space straight i with hat on top minus space 4.0 straight t space space straight j with hat on top Acceleration space of space the space particle space is space given space by comma straight a with bar on top space equals space fraction numerator straight d straight v with rightwards harpoon with barb upwards on top over denominator dt end fraction space equals space straight d over dt open parentheses space 3.0 space straight i with hat on top minus space 4.0 straight t space space straight j with hat on top close parentheses space straight a with bar on top space equals space minus space 4.0 space space straight j with hat on top space

Some More Questions From Motion in A Plane Chapter

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

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.

What are axial 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

The position of a particle is given by where t is in seconds and the coefficients have the proper units for r to be in metres.(a) Find the v and a of the particle?

Some More Questions From Motion in A Plane Chapter

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.

What are axial 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.