QBManager

Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is $4 π m$ , is (Assume the forward direction as $x$ -axis)

1

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

2

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

3

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

4

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

Explanation:

$S = \sqrt{y^{2} + x^{2}}$ and $θ = \tan^{- 1} ◻ \frac{y}{\exists x} ◻$

Motion in Plane

269947 A particle starts from the origin at $t = 0 s$ with a velocity of $10.0 \hat{j} m / s$ and moves in the $x y$ -plane with a constant acceleration of $(8 \hat{i} + 2 \hat{j}) {ms}^{- 2}$ . Then $y$ -coordinate of the particle in $2 \sec$ is

1

24 m

2

16 m

3

8 m

4

12 m

Explanation:

$\vec{r} = {\vec{v}}_{0} t + \frac{1}{2} \vec{a} t^{2}, y (t) = t^{2} + 10 t$

Motion in Plane

269948 A car moving at a constant speed of $36 kmph$ moves north wards for 20 minutes then due to west with the same speed for $8 \frac{1}{3}$ minutes. what is the average velocity of the car during this run in $k m p h$

1 27.5

2 40.5

3 20.8

4 32.7

Explanation:

$v_{avg} = \frac{\vec{v_{1}} t_{1} + {\vec{v}}_{2} t_{2}}{t_{1} + t_{2}}$

Motion in Plane

269949 Velocity of a particle at time $t = 0$ is $2 {ms}^{- 1}$ . A constant acceleration of $2 {ms}^{- 2}$ acts on the particle for 1 second at an angle of $60^{\circ}$ with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1

\sqrt{3} m / s

2

2 \sqrt{3} m / s

3

4 m / s

4

8 m / s

Explanation:

$\vec{v} = v_{x} \hat{i} + v_{y} \hat{j} : v_{x} = u_{x} + a_{x} t, v_{y} = u_{y} + a_{y} t$ $a_{x} = a \cos θ, a_{y} = a \sin θ$

Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is $4 π m$ , is (Assume the forward direction as $x$ -axis)

1

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

2

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

3

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

4

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

Explanation:

$S = \sqrt{y^{2} + x^{2}}$ and $θ = \tan^{- 1} ◻ \frac{y}{\exists x} ◻$

Motion in Plane

269947 A particle starts from the origin at $t = 0 s$ with a velocity of $10.0 \hat{j} m / s$ and moves in the $x y$ -plane with a constant acceleration of $(8 \hat{i} + 2 \hat{j}) {ms}^{- 2}$ . Then $y$ -coordinate of the particle in $2 \sec$ is

1

24 m

2

16 m

3

8 m

4

12 m

Explanation:

$\vec{r} = {\vec{v}}_{0} t + \frac{1}{2} \vec{a} t^{2}, y (t) = t^{2} + 10 t$

Motion in Plane

269948 A car moving at a constant speed of $36 kmph$ moves north wards for 20 minutes then due to west with the same speed for $8 \frac{1}{3}$ minutes. what is the average velocity of the car during this run in $k m p h$

1 27.5

2 40.5

3 20.8

4 32.7

Explanation:

$v_{avg} = \frac{\vec{v_{1}} t_{1} + {\vec{v}}_{2} t_{2}}{t_{1} + t_{2}}$

Motion in Plane

269949 Velocity of a particle at time $t = 0$ is $2 {ms}^{- 1}$ . A constant acceleration of $2 {ms}^{- 2}$ acts on the particle for 1 second at an angle of $60^{\circ}$ with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1

\sqrt{3} m / s

2

2 \sqrt{3} m / s

3

4 m / s

4

8 m / s

Explanation:

$\vec{v} = v_{x} \hat{i} + v_{y} \hat{j} : v_{x} = u_{x} + a_{x} t, v_{y} = u_{y} + a_{y} t$ $a_{x} = a \cos θ, a_{y} = a \sin θ$

Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is $4 π m$ , is (Assume the forward direction as $x$ -axis)

1

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

2

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

3

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

4

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

Explanation:

$S = \sqrt{y^{2} + x^{2}}$ and $θ = \tan^{- 1} ◻ \frac{y}{\exists x} ◻$

Motion in Plane

269947 A particle starts from the origin at $t = 0 s$ with a velocity of $10.0 \hat{j} m / s$ and moves in the $x y$ -plane with a constant acceleration of $(8 \hat{i} + 2 \hat{j}) {ms}^{- 2}$ . Then $y$ -coordinate of the particle in $2 \sec$ is

1

24 m

2

16 m

3

8 m

4

12 m

Explanation:

$\vec{r} = {\vec{v}}_{0} t + \frac{1}{2} \vec{a} t^{2}, y (t) = t^{2} + 10 t$

Motion in Plane

269948 A car moving at a constant speed of $36 kmph$ moves north wards for 20 minutes then due to west with the same speed for $8 \frac{1}{3}$ minutes. what is the average velocity of the car during this run in $k m p h$

1 27.5

2 40.5

3 20.8

4 32.7

Explanation:

$v_{avg} = \frac{\vec{v_{1}} t_{1} + {\vec{v}}_{2} t_{2}}{t_{1} + t_{2}}$

Motion in Plane

269949 Velocity of a particle at time $t = 0$ is $2 {ms}^{- 1}$ . A constant acceleration of $2 {ms}^{- 2}$ acts on the particle for 1 second at an angle of $60^{\circ}$ with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1

\sqrt{3} m / s

2

2 \sqrt{3} m / s

3

4 m / s

4

8 m / s

Explanation:

$\vec{v} = v_{x} \hat{i} + v_{y} \hat{j} : v_{x} = u_{x} + a_{x} t, v_{y} = u_{y} + a_{y} t$ $a_{x} = a \cos θ, a_{y} = a \sin θ$

Motion in Plane

269946 The displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward quarter revolution where perimeter of the wheel is $4 π m$ , is (Assume the forward direction as $x$ -axis)

1

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

2

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

3

\sqrt{(π - 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π}

with

x

- axis

4

\sqrt{(π + 2)^{2} + 4}

along

\tan^{- 1} \frac{2}{π - 2}

with

x

- axis

Explanation:

$S = \sqrt{y^{2} + x^{2}}$ and $θ = \tan^{- 1} ◻ \frac{y}{\exists x} ◻$

Motion in Plane

269947 A particle starts from the origin at $t = 0 s$ with a velocity of $10.0 \hat{j} m / s$ and moves in the $x y$ -plane with a constant acceleration of $(8 \hat{i} + 2 \hat{j}) {ms}^{- 2}$ . Then $y$ -coordinate of the particle in $2 \sec$ is

1

24 m

2

16 m

3

8 m

4

12 m

Explanation:

$\vec{r} = {\vec{v}}_{0} t + \frac{1}{2} \vec{a} t^{2}, y (t) = t^{2} + 10 t$

Motion in Plane

269948 A car moving at a constant speed of $36 kmph$ moves north wards for 20 minutes then due to west with the same speed for $8 \frac{1}{3}$ minutes. what is the average velocity of the car during this run in $k m p h$

1 27.5

2 40.5

3 20.8

4 32.7

Explanation:

$v_{avg} = \frac{\vec{v_{1}} t_{1} + {\vec{v}}_{2} t_{2}}{t_{1} + t_{2}}$

Motion in Plane

269949 Velocity of a particle at time $t = 0$ is $2 {ms}^{- 1}$ . A constant acceleration of $2 {ms}^{- 2}$ acts on the particle for 1 second at an angle of $60^{\circ}$ with its initial velocity. Find the magnitude of velocity at the end of 1 second.

1

\sqrt{3} m / s

2

2 \sqrt{3} m / s

3

4 m / s

4

8 m / s

Explanation:

$\vec{v} = v_{x} \hat{i} + v_{y} \hat{j} : v_{x} = u_{x} + a_{x} t, v_{y} = u_{y} + a_{y} t$ $a_{x} = a \cos θ, a_{y} = a \sin θ$

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Question Bank Series

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