MOTION IN A PLANE
Motion in Plane

269866 A body starts with a velocity\((2 \hat{i}+3 \hat{j}+11 \hat{k}) \mathrm{m} / \mathrm{s}\) and moves with an acceleration \((5 \hat{i}+5 \hat{j}-5 \hat{k}) \mathrm{m} / \mathrm{s}^{2}\). 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 \(3 \hat{i}+4 \hat{j}+10 \hat{k}\)
Motion in Plane

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

1 \(500 \mathrm{~m}\)
2 \(400 \mathrm{~m}\)
3 \(300 \mathrm{~m}\)
4 \(700 \mathrm{~m}\)
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 \(4 \hat{i}+2 \hat{j}+2 \hat{k} \mathrm{~ms}^{-1}\), the mass of the body

1 \(20 \mathrm{~kg}\)
2 \(15 \mathrm{~kg}\)
3 \(10 \mathrm{~kg}\)
4 \(5 \mathrm{~kg}\)
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 \(1 \mathrm{~s}\) to \(3 \mathrm{~s}\) 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 \(32 \hat{j}-26 \hat{k}\)
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 \(10 \mathrm{sec}\). 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 \(\frac{-\vec{j}+\vec{k}}{5}\)
Motion in Plane

269866 A body starts with a velocity\((2 \hat{i}+3 \hat{j}+11 \hat{k}) \mathrm{m} / \mathrm{s}\) and moves with an acceleration \((5 \hat{i}+5 \hat{j}-5 \hat{k}) \mathrm{m} / \mathrm{s}^{2}\). 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 \(3 \hat{i}+4 \hat{j}+10 \hat{k}\)
Motion in Plane

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

1 \(500 \mathrm{~m}\)
2 \(400 \mathrm{~m}\)
3 \(300 \mathrm{~m}\)
4 \(700 \mathrm{~m}\)
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 \(4 \hat{i}+2 \hat{j}+2 \hat{k} \mathrm{~ms}^{-1}\), the mass of the body

1 \(20 \mathrm{~kg}\)
2 \(15 \mathrm{~kg}\)
3 \(10 \mathrm{~kg}\)
4 \(5 \mathrm{~kg}\)
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 \(1 \mathrm{~s}\) to \(3 \mathrm{~s}\) 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 \(32 \hat{j}-26 \hat{k}\)
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 \(10 \mathrm{sec}\). 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 \(\frac{-\vec{j}+\vec{k}}{5}\)
Motion in Plane

269866 A body starts with a velocity\((2 \hat{i}+3 \hat{j}+11 \hat{k}) \mathrm{m} / \mathrm{s}\) and moves with an acceleration \((5 \hat{i}+5 \hat{j}-5 \hat{k}) \mathrm{m} / \mathrm{s}^{2}\). 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 \(3 \hat{i}+4 \hat{j}+10 \hat{k}\)
Motion in Plane

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

1 \(500 \mathrm{~m}\)
2 \(400 \mathrm{~m}\)
3 \(300 \mathrm{~m}\)
4 \(700 \mathrm{~m}\)
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 \(4 \hat{i}+2 \hat{j}+2 \hat{k} \mathrm{~ms}^{-1}\), the mass of the body

1 \(20 \mathrm{~kg}\)
2 \(15 \mathrm{~kg}\)
3 \(10 \mathrm{~kg}\)
4 \(5 \mathrm{~kg}\)
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 \(1 \mathrm{~s}\) to \(3 \mathrm{~s}\) 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 \(32 \hat{j}-26 \hat{k}\)
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 \(10 \mathrm{sec}\). 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 \(\frac{-\vec{j}+\vec{k}}{5}\)
Motion in Plane

269866 A body starts with a velocity\((2 \hat{i}+3 \hat{j}+11 \hat{k}) \mathrm{m} / \mathrm{s}\) and moves with an acceleration \((5 \hat{i}+5 \hat{j}-5 \hat{k}) \mathrm{m} / \mathrm{s}^{2}\). 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 \(3 \hat{i}+4 \hat{j}+10 \hat{k}\)
Motion in Plane

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

1 \(500 \mathrm{~m}\)
2 \(400 \mathrm{~m}\)
3 \(300 \mathrm{~m}\)
4 \(700 \mathrm{~m}\)
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 \(4 \hat{i}+2 \hat{j}+2 \hat{k} \mathrm{~ms}^{-1}\), the mass of the body

1 \(20 \mathrm{~kg}\)
2 \(15 \mathrm{~kg}\)
3 \(10 \mathrm{~kg}\)
4 \(5 \mathrm{~kg}\)
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 \(1 \mathrm{~s}\) to \(3 \mathrm{~s}\) 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 \(32 \hat{j}-26 \hat{k}\)
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 \(10 \mathrm{sec}\). 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 \(\frac{-\vec{j}+\vec{k}}{5}\)
Motion in Plane

269866 A body starts with a velocity\((2 \hat{i}+3 \hat{j}+11 \hat{k}) \mathrm{m} / \mathrm{s}\) and moves with an acceleration \((5 \hat{i}+5 \hat{j}-5 \hat{k}) \mathrm{m} / \mathrm{s}^{2}\). 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 \(3 \hat{i}+4 \hat{j}+10 \hat{k}\)
Motion in Plane

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

1 \(500 \mathrm{~m}\)
2 \(400 \mathrm{~m}\)
3 \(300 \mathrm{~m}\)
4 \(700 \mathrm{~m}\)
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 \(4 \hat{i}+2 \hat{j}+2 \hat{k} \mathrm{~ms}^{-1}\), the mass of the body

1 \(20 \mathrm{~kg}\)
2 \(15 \mathrm{~kg}\)
3 \(10 \mathrm{~kg}\)
4 \(5 \mathrm{~kg}\)
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 \(1 \mathrm{~s}\) to \(3 \mathrm{~s}\) 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 \(32 \hat{j}-26 \hat{k}\)
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 \(10 \mathrm{sec}\). 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 \(\frac{-\vec{j}+\vec{k}}{5}\)