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.

(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

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Solution

Velocity space vector space is comma space straight v with rightwards harpoon with barb upwards on top space equals space 3.0 space straight i with hat on top space minus space 4.0 space straight j with hat on top space At space straight t space equals space 2.0 space sec straight v with rightwards harpoon with barb upwards on top space equals space 3.0 space straight i with hat on top space minus 8.0 space straight j with hat on top space Magnitude space of space velocity comma space open vertical bar straight v with rightwards harpoon with barb upwards on top close vertical bar space equals space square root of left parenthesis 3 right parenthesis squared plus left parenthesis negative 8 right parenthesis squared end root space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals square root of 73 space equals 8.54 space straight m divided by straight s Direction comma space straight theta space equals space tan to the power of negative 1 end exponent space open parentheses straight v subscript straight y over straight v subscript straight x close parentheses space space space space space space space space space space space space space space space space space space space space space space space equals space tan to the power of negative 1 end exponent space open parentheses negative 8 over 3 close parentheses space space space space space space space space space space space space space space space space space space space space space space space equals negative space space tan to the power of negative 1 end exponent space left parenthesis 2.667 right parenthesis space space space space space space space space space space space space space space space space space space space space space space equals space minus 69.45 to the power of straight o Negative space sign space indicates space that space the space direction space of space velocity space is space below space the space straight x minus axis.

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Motion In A Plane

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.

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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.(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

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

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.