QBManager

Motion in Plane

269866 A body starts with a velocity $(2 \hat{i} + 3 \hat{j} + 11 \hat{k}) m / s$ and moves with an acceleration $(5 \hat{i} + 5 \hat{j} - 5 \hat{k}) m / s^{2}$ . What is its velocity after 0.2 sec?

1

7 \hat{i} + 8 \hat{j} + 6 \hat{k}

2

2 \hat{i} - 3 \hat{j} + 11 \hat{k}

3

3 \hat{i} - 4 \hat{j} - 10 \hat{k}

4

3 \hat{i} + 4 \hat{j} + 10 \hat{k}

Explanation:

$\hat{v} = \hat{u} + \hat{a} . t$

Motion in Plane

269867 The position vector of a particle is given by $\vec{r} = (3 t^{2} \hat{i} + 4 t^{2} \hat{j} + 7 \hat{k}) m$ at a given time $t$ . The net displacement of the particle after $10 s$ is

1

500 m

2

400 m

3

300 m

4

700 m

Explanation:

At $t = 0, {\vec{r}}_{1} = 7 \vec{k}$
At $t = 10, {\vec{r}}_{2} = 300 \vec{i} + 400 \vec{j} + 7 \vec{k}; \vec{s} = {\vec{r}}_{2} - {\vec{r}}_{1}$

Motion in Plane

269906 A force $2 \hat{i} + \hat{j} - \hat{k}$ newton acts on a body which is initially at rest. If the velocity of the body at the end of 20 seconds is $4 \hat{i} + 2 \hat{j} + 2 \hat{k} {ms}^{- 1}$ , the mass of the body

1

20 kg

2

15 kg

3

10 kg

4

5 kg

Explanation:

$\vec{v} = (\vec{a}) t$ , and $\vec{f} = m \vec{a}$

Motion in Plane

269907 The position vector of a moving particle at seconds is given by $\vec{r} = 3 \hat{i} + 4 t^{2} \hat{j} - t^{3} \hat{k}$ . Its displacement during an interval of $1 s$ to $3 s$ is

1

\hat{j} - \hat{k}

2

3 \hat{i} + 4 \hat{j} - \hat{k}

3

9 \hat{i} + 36 \hat{j} - 27 \hat{k}

4

32 \hat{j} - 26 \hat{k}

Explanation:

Position vector at $(t = 1 \sec)$ is ${\vec{r}}_{1}$
Position vector at ( $t = 3 \sec$ ) is $\vec{r_{3}}$
Displacement $\vec{s} = {\vec{r}}_{3} - {\vec{r}}_{11}$

Motion in Plane

269908 If initial velocity of a body is $\vec{u} = 2 \vec{i} - 2 \vec{j} + 3 \vec{k}$ and the final velocity is $\vec{v} = 2 \vec{i} - 4 \vec{j} + 5 \vec{k}$ and it is changed in time of $10 \sec$ . Find the acceleration vector?

1

\frac{3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

2

\frac{- 3 \vec{i} + \vec{j} + 2 \vec{k}}{10}

3

\frac{- 3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

4

\frac{- \vec{j} + \vec{k}}{5}

Explanation:

$\vec{a} = \frac{\vec{v} - \vec{u}}{t}$

Motion in Plane

269866 A body starts with a velocity $(2 \hat{i} + 3 \hat{j} + 11 \hat{k}) m / s$ and moves with an acceleration $(5 \hat{i} + 5 \hat{j} - 5 \hat{k}) m / s^{2}$ . What is its velocity after 0.2 sec?

1

7 \hat{i} + 8 \hat{j} + 6 \hat{k}

2

2 \hat{i} - 3 \hat{j} + 11 \hat{k}

3

3 \hat{i} - 4 \hat{j} - 10 \hat{k}

4

3 \hat{i} + 4 \hat{j} + 10 \hat{k}

Explanation:

$\hat{v} = \hat{u} + \hat{a} . t$

Motion in Plane

269867 The position vector of a particle is given by $\vec{r} = (3 t^{2} \hat{i} + 4 t^{2} \hat{j} + 7 \hat{k}) m$ at a given time $t$ . The net displacement of the particle after $10 s$ is

1

500 m

2

400 m

3

300 m

4

700 m

Explanation:

At $t = 0, {\vec{r}}_{1} = 7 \vec{k}$
At $t = 10, {\vec{r}}_{2} = 300 \vec{i} + 400 \vec{j} + 7 \vec{k}; \vec{s} = {\vec{r}}_{2} - {\vec{r}}_{1}$

Motion in Plane

269906 A force $2 \hat{i} + \hat{j} - \hat{k}$ newton acts on a body which is initially at rest. If the velocity of the body at the end of 20 seconds is $4 \hat{i} + 2 \hat{j} + 2 \hat{k} {ms}^{- 1}$ , the mass of the body

1

20 kg

2

15 kg

3

10 kg

4

5 kg

Explanation:

$\vec{v} = (\vec{a}) t$ , and $\vec{f} = m \vec{a}$

Motion in Plane

269907 The position vector of a moving particle at seconds is given by $\vec{r} = 3 \hat{i} + 4 t^{2} \hat{j} - t^{3} \hat{k}$ . Its displacement during an interval of $1 s$ to $3 s$ is

1

\hat{j} - \hat{k}

2

3 \hat{i} + 4 \hat{j} - \hat{k}

3

9 \hat{i} + 36 \hat{j} - 27 \hat{k}

4

32 \hat{j} - 26 \hat{k}

Explanation:

Position vector at $(t = 1 \sec)$ is ${\vec{r}}_{1}$
Position vector at ( $t = 3 \sec$ ) is $\vec{r_{3}}$
Displacement $\vec{s} = {\vec{r}}_{3} - {\vec{r}}_{11}$

Motion in Plane

269908 If initial velocity of a body is $\vec{u} = 2 \vec{i} - 2 \vec{j} + 3 \vec{k}$ and the final velocity is $\vec{v} = 2 \vec{i} - 4 \vec{j} + 5 \vec{k}$ and it is changed in time of $10 \sec$ . Find the acceleration vector?

1

\frac{3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

2

\frac{- 3 \vec{i} + \vec{j} + 2 \vec{k}}{10}

3

\frac{- 3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

4

\frac{- \vec{j} + \vec{k}}{5}

Explanation:

$\vec{a} = \frac{\vec{v} - \vec{u}}{t}$

Motion in Plane

269866 A body starts with a velocity $(2 \hat{i} + 3 \hat{j} + 11 \hat{k}) m / s$ and moves with an acceleration $(5 \hat{i} + 5 \hat{j} - 5 \hat{k}) m / s^{2}$ . What is its velocity after 0.2 sec?

1

7 \hat{i} + 8 \hat{j} + 6 \hat{k}

2

2 \hat{i} - 3 \hat{j} + 11 \hat{k}

3

3 \hat{i} - 4 \hat{j} - 10 \hat{k}

4

3 \hat{i} + 4 \hat{j} + 10 \hat{k}

Explanation:

$\hat{v} = \hat{u} + \hat{a} . t$

Motion in Plane

269867 The position vector of a particle is given by $\vec{r} = (3 t^{2} \hat{i} + 4 t^{2} \hat{j} + 7 \hat{k}) m$ at a given time $t$ . The net displacement of the particle after $10 s$ is

1

500 m

2

400 m

3

300 m

4

700 m

Explanation:

At $t = 0, {\vec{r}}_{1} = 7 \vec{k}$
At $t = 10, {\vec{r}}_{2} = 300 \vec{i} + 400 \vec{j} + 7 \vec{k}; \vec{s} = {\vec{r}}_{2} - {\vec{r}}_{1}$

Motion in Plane

269906 A force $2 \hat{i} + \hat{j} - \hat{k}$ newton acts on a body which is initially at rest. If the velocity of the body at the end of 20 seconds is $4 \hat{i} + 2 \hat{j} + 2 \hat{k} {ms}^{- 1}$ , the mass of the body

1

20 kg

2

15 kg

3

10 kg

4

5 kg

Explanation:

$\vec{v} = (\vec{a}) t$ , and $\vec{f} = m \vec{a}$

Motion in Plane

269907 The position vector of a moving particle at seconds is given by $\vec{r} = 3 \hat{i} + 4 t^{2} \hat{j} - t^{3} \hat{k}$ . Its displacement during an interval of $1 s$ to $3 s$ is

1

\hat{j} - \hat{k}

2

3 \hat{i} + 4 \hat{j} - \hat{k}

3

9 \hat{i} + 36 \hat{j} - 27 \hat{k}

4

32 \hat{j} - 26 \hat{k}

Explanation:

Position vector at $(t = 1 \sec)$ is ${\vec{r}}_{1}$
Position vector at ( $t = 3 \sec$ ) is $\vec{r_{3}}$
Displacement $\vec{s} = {\vec{r}}_{3} - {\vec{r}}_{11}$

Motion in Plane

269908 If initial velocity of a body is $\vec{u} = 2 \vec{i} - 2 \vec{j} + 3 \vec{k}$ and the final velocity is $\vec{v} = 2 \vec{i} - 4 \vec{j} + 5 \vec{k}$ and it is changed in time of $10 \sec$ . Find the acceleration vector?

1

\frac{3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

2

\frac{- 3 \vec{i} + \vec{j} + 2 \vec{k}}{10}

3

\frac{- 3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

4

\frac{- \vec{j} + \vec{k}}{5}

Explanation:

$\vec{a} = \frac{\vec{v} - \vec{u}}{t}$

Motion in Plane

269866 A body starts with a velocity $(2 \hat{i} + 3 \hat{j} + 11 \hat{k}) m / s$ and moves with an acceleration $(5 \hat{i} + 5 \hat{j} - 5 \hat{k}) m / s^{2}$ . What is its velocity after 0.2 sec?

1

7 \hat{i} + 8 \hat{j} + 6 \hat{k}

2

2 \hat{i} - 3 \hat{j} + 11 \hat{k}

3

3 \hat{i} - 4 \hat{j} - 10 \hat{k}

4

3 \hat{i} + 4 \hat{j} + 10 \hat{k}

Explanation:

$\hat{v} = \hat{u} + \hat{a} . t$

Motion in Plane

269867 The position vector of a particle is given by $\vec{r} = (3 t^{2} \hat{i} + 4 t^{2} \hat{j} + 7 \hat{k}) m$ at a given time $t$ . The net displacement of the particle after $10 s$ is

1

500 m

2

400 m

3

300 m

4

700 m

Explanation:

At $t = 0, {\vec{r}}_{1} = 7 \vec{k}$
At $t = 10, {\vec{r}}_{2} = 300 \vec{i} + 400 \vec{j} + 7 \vec{k}; \vec{s} = {\vec{r}}_{2} - {\vec{r}}_{1}$

Motion in Plane

269906 A force $2 \hat{i} + \hat{j} - \hat{k}$ newton acts on a body which is initially at rest. If the velocity of the body at the end of 20 seconds is $4 \hat{i} + 2 \hat{j} + 2 \hat{k} {ms}^{- 1}$ , the mass of the body

1

20 kg

2

15 kg

3

10 kg

4

5 kg

Explanation:

$\vec{v} = (\vec{a}) t$ , and $\vec{f} = m \vec{a}$

Motion in Plane

269907 The position vector of a moving particle at seconds is given by $\vec{r} = 3 \hat{i} + 4 t^{2} \hat{j} - t^{3} \hat{k}$ . Its displacement during an interval of $1 s$ to $3 s$ is

1

\hat{j} - \hat{k}

2

3 \hat{i} + 4 \hat{j} - \hat{k}

3

9 \hat{i} + 36 \hat{j} - 27 \hat{k}

4

32 \hat{j} - 26 \hat{k}

Explanation:

Position vector at $(t = 1 \sec)$ is ${\vec{r}}_{1}$
Position vector at ( $t = 3 \sec$ ) is $\vec{r_{3}}$
Displacement $\vec{s} = {\vec{r}}_{3} - {\vec{r}}_{11}$

Motion in Plane

269908 If initial velocity of a body is $\vec{u} = 2 \vec{i} - 2 \vec{j} + 3 \vec{k}$ and the final velocity is $\vec{v} = 2 \vec{i} - 4 \vec{j} + 5 \vec{k}$ and it is changed in time of $10 \sec$ . Find the acceleration vector?

1

\frac{3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

2

\frac{- 3 \vec{i} + \vec{j} + 2 \vec{k}}{10}

3

\frac{- 3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

4

\frac{- \vec{j} + \vec{k}}{5}

Explanation:

$\vec{a} = \frac{\vec{v} - \vec{u}}{t}$

Motion in Plane

269866 A body starts with a velocity $(2 \hat{i} + 3 \hat{j} + 11 \hat{k}) m / s$ and moves with an acceleration $(5 \hat{i} + 5 \hat{j} - 5 \hat{k}) m / s^{2}$ . What is its velocity after 0.2 sec?

1

7 \hat{i} + 8 \hat{j} + 6 \hat{k}

2

2 \hat{i} - 3 \hat{j} + 11 \hat{k}

3

3 \hat{i} - 4 \hat{j} - 10 \hat{k}

4

3 \hat{i} + 4 \hat{j} + 10 \hat{k}

Explanation:

$\hat{v} = \hat{u} + \hat{a} . t$

Motion in Plane

269867 The position vector of a particle is given by $\vec{r} = (3 t^{2} \hat{i} + 4 t^{2} \hat{j} + 7 \hat{k}) m$ at a given time $t$ . The net displacement of the particle after $10 s$ is

1

500 m

2

400 m

3

300 m

4

700 m

Explanation:

At $t = 0, {\vec{r}}_{1} = 7 \vec{k}$
At $t = 10, {\vec{r}}_{2} = 300 \vec{i} + 400 \vec{j} + 7 \vec{k}; \vec{s} = {\vec{r}}_{2} - {\vec{r}}_{1}$

Motion in Plane

269906 A force $2 \hat{i} + \hat{j} - \hat{k}$ newton acts on a body which is initially at rest. If the velocity of the body at the end of 20 seconds is $4 \hat{i} + 2 \hat{j} + 2 \hat{k} {ms}^{- 1}$ , the mass of the body

1

20 kg

2

15 kg

3

10 kg

4

5 kg

Explanation:

$\vec{v} = (\vec{a}) t$ , and $\vec{f} = m \vec{a}$

Motion in Plane

269907 The position vector of a moving particle at seconds is given by $\vec{r} = 3 \hat{i} + 4 t^{2} \hat{j} - t^{3} \hat{k}$ . Its displacement during an interval of $1 s$ to $3 s$ is

1

\hat{j} - \hat{k}

2

3 \hat{i} + 4 \hat{j} - \hat{k}

3

9 \hat{i} + 36 \hat{j} - 27 \hat{k}

4

32 \hat{j} - 26 \hat{k}

Explanation:

Position vector at $(t = 1 \sec)$ is ${\vec{r}}_{1}$
Position vector at ( $t = 3 \sec$ ) is $\vec{r_{3}}$
Displacement $\vec{s} = {\vec{r}}_{3} - {\vec{r}}_{11}$

Motion in Plane

269908 If initial velocity of a body is $\vec{u} = 2 \vec{i} - 2 \vec{j} + 3 \vec{k}$ and the final velocity is $\vec{v} = 2 \vec{i} - 4 \vec{j} + 5 \vec{k}$ and it is changed in time of $10 \sec$ . Find the acceleration vector?

1

\frac{3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

2

\frac{- 3 \vec{i} + \vec{j} + 2 \vec{k}}{10}

3

\frac{- 3 \vec{i} - 2 \vec{j} + 2 \vec{k}}{10}

4

\frac{- \vec{j} + \vec{k}}{5}

Explanation:

$\vec{a} = \frac{\vec{v} - \vec{u}}{t}$