A particle is moving along x-axis. The velocity v of particle varies with its position x as $\mathrm{v}=\frac{1}{\mathrm{x}}$. Find velocity of particle as a function of time t given that at t=0, x=1 .

1.  $\mathrm{v}=\sqrt{2\mathrm{t}+1}$

2.  $\mathrm{v}=\frac{1}{\sqrt{2\mathrm{t}+1}}$

3.  $\mathrm{v}=\frac{1}{\mathrm{t}}$

4.  None of these

Concept Questions :-

Integration
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Difficulty Level:

A vector $\stackrel{\to }{\mathrm{A}}$ is directed along $30°$ west of north direction and another vector $\stackrel{\to }{\mathrm{B}}$ along $15°$ south of east. Their resultant cannot be in ____________ direction.

(A)  North

(B)  East

(C)  North-East

(D)  South

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

ABCD is a quadrilateral. Forces  act at a point. Their resultant is

(A)

(B)

(C)  zero vector

(D)

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

The resultant of the forces $\stackrel{\to }{\mathrm{P}}$ and $\stackrel{\to }{\mathrm{Q}}$ is $\stackrel{\to }{\mathrm{R}}$. If $\stackrel{\to }{\mathrm{Q}}$ is double then the resultant also doubles in magnitude. Find the angle between $\stackrel{\to }{\mathrm{P}}$ and $\stackrel{\to }{\mathrm{Q}}$.

(A)

(B)

(C)

(D)

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

The maximum and minimum magnitude of the resultant of two vectors are 17 units and 7 units respectively. Then the magnitude of resultant of the vectors when they act perpendicular to each other is:

(A)  14

(B)  16

(C)  18

(D)  13

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

A vector $\stackrel{\to }{\mathrm{A}}$ makes an angle of $20°$ and $\stackrel{\to }{\mathrm{B}}$ makes an angle of $110°$ with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the magnitude of the resultant.

(A)  $1$

(B)  $5\sqrt{2}$

(C)  $5$

(D)  $7$

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

A particle is moving westward with a velocity  Its velocity changed to ${\stackrel{\to }{\mathrm{v}}}_{2}=5\mathrm{m}/\mathrm{s}$ northward. The change in velocity vector $\left(∆\stackrel{\to }{\mathrm{V}}={\stackrel{\to }{\mathrm{v}}}_{2}-{\stackrel{\to }{\mathrm{v}}}_{1}\right)$ is:

(A)   towards north east

(B)   towards north west

(C)  zero

(D)  towards north west

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

Consider east as positive x-axis, north as positive y-axis and vertically upward direction as z-axis. A helicopter first rises up to an altitude of 100 m than flies straight in north 500 m and then suddenly takes a turn towards east and travels 1000 m east. What is position vector of helicopter. (Take starting point as origin)

(A)

(B)

(C)

(D)

Concept Questions :-

Resultant of Vectors
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Difficulty Level:

A force $\stackrel{\to }{\mathrm{F}}=6\stackrel{^}{\mathrm{i}}-8\stackrel{^}{\mathrm{j}}+10\stackrel{^}{\mathrm{k}}$ Newton produces acceleration  in a body. The mass of the body is (in kg)

(A)  $6\stackrel{^}{\mathrm{i}}-8\stackrel{^}{\mathrm{j}}+10\stackrel{^}{\mathrm{k}}$

(B)  $100$

(C)  $10\sqrt{2}$

(D)  $10$

Concept Questions :-

Resultant of Vectors
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

angle between $\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$ is

(A)  $120°$

(B)  $90°$

(C)  $60°$

(D)  $30°$

Concept Questions :-

Scalar Product