The position of particle at any instant is given by . At what instant the velocity vector will make an angle 45° with X-axis? - Wired Faculty

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The position of particle at any instant is given by $straight r with rightwards arrow on top equals 50 straight t straight j with hat on top plus 5 straight t squared straight i with hat on top$ . At what instant the velocity vector will make an angle 45° with X-axis?

Solution

Given,
Position of the particle, $straight r with rightwards arrow on top space equals space 50 straight t straight j with hat on top plus 5 straight t squared straight i with hat on top$
∴ Velocity, $straight v with rightwards arrow on top equals straight d over dt left parenthesis straight r with rightwards arrow on top right parenthesis space equals space straight d over dt left parenthesis 50 straight t space straight j with hat on top plus 5 straight t squared straight i with hat on top right parenthesis$
$equals 50 straight j with hat on top plus 10 straight t space straight i with hat on top$
The angle which the velocity vector makes with X-axis at any instant is,
$tanθ space equals space straight v subscript straight y over straight v subscript straight x equals fraction numerator 50 over denominator 10 straight t end fraction$
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Therefore,
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$rightwards double arrow$ $straight t equals 5 straight s$
So, when time is 5 seconds, the velocity vector will make an angle 45⁰ with x-axis.

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Motion In A Plane

The position of particle at any instant is given by $straight r with rightwards arrow on top equals 50 straight t straight j with hat on top plus 5 straight t squared straight i with hat on top$ . At what instant the velocity vector will make an angle 45° with X-axis?

Some More Questions From Motion in A Plane Chapter

Pick out the only vector quantities in the following list:
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For Daily Free Study Material Join wiredfaculty

Motion In A Plane

The position of particle at any instant is given by . At what instant the velocity vector will make an angle 45° with X-axis?

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.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

Give two examples of axial vectors.

What are tensors?

Give one example of tensor.

What is module of vector?

What are equal vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The position of particle at any instant is given by $straight r with rightwards arrow on top equals 50 straight t straight j with hat on top plus 5 straight t squared straight i with hat on top$ . At what instant the velocity vector will make an angle 45° with X-axis?

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.