Position of a point

Q. Initially the origin was at $X=0$ and position of a particle at point $P$ was given as $X=-3\text{m}$, if origin is shifted by $1$ unit to the left, then position of point $P$ with respect to new origin will be:

1. $4\text{m}$
2. $-4\text{m}$
3. $-2\text{m}$
4. $-3\text{m}$

Q. In the given figure, what is the position of point A from origin ?

Q. At $t=0$, a particle starts from $(4,0)$ and moves towards positive $x-$axis with speed of $v=8t+3\text{m/s}$. The final position of the particle as a function of time is

1. $4t^2-3t-4\text{m}$
2. $4t^2-3t+4\text{m}$
3. $4t^2+3t+4\text{m}$
4. $4t^2-3t\text{m}$

Q. Three balls initially at rest are released from the origin in the same direction and covers a distance of $5\text{m}$, $9\text{m}$ and $15\text{m}$ respectively. What will be the position of the ball farthest from the origin w.r.t the ball nearest to the origin?

1. $4\text{m}$
2. $6\text{m}$
3. $9\text{m}$
4. $10\text{m}$

Q. In the given figure, what is the position of point A from origin ?

Q. An insect is moving on a rectangular plane from one vertex point to other along the diagonal, How many minimum number of independent informations required to completely specify its position.

1. $1$
2. $2$
3. $3$
4. $\text{None of the above}$

Q. Instantaneous velocity of an object varies with time as $v=\alpha -\beta t^2$. Find its position, $x$ as a function of time, $t$. Also find the object`s maximum positive displacement, $x_{max}$ from the origin.

1. $x=\alpha t-\frac{\beta t^3}{3}$ and $x_{max}=\frac{2}{3}\frac{{\alpha }^{3/2}}{{\beta }^{3/2}}$
2. $x=\alpha t-\frac{\beta t^3}{3}$ and $x_{max}=\frac{2\alpha }{{\beta }^{1/2}}$
3. $x=2\alpha t-\beta$ and $x_{max}=2\alpha \beta$
4. $x=2{\alpha }^{2}t-\beta t^3$ and $x_{max}=\frac{2{\alpha }^{1/2}}{{\beta }^{3/2}}$

Q. Can I just use the amount I turn my head as the measure for how far a body is moving?

1. No
2. Yes

Q. If position of $B$ with respect to $P$, is $+2\text{m}$ and position of $C$ with respect to $P$ is $-4\text{m}$. Where $B,P,C$ are the points along $X-$axis, then what will be the position of $B$ with respect to $C$ ?

1. $3\text{m}$
2. $6\text{m}$
3. $-5\text{m}$
4. $-2\text{m}$

Q. Initially the origin was at $X=0$ and position of a particle at point $P$ was given as $X=-3\text{m}$, if origin is shifted by $1$ unit to the left, then position of point $P$ with respect to new origin will be:

1. $4\text{m}$
2. $-4\text{m}$
3. $-2\text{m}$
4. $-3\text{m}$

Q. A particle starting from the origin $(0,0)$ moves in a straight line in the $(x,y)$ plane. Its coordinates at a later time are $(\sqrt{3},3)$. The path of the particle makes with the x-axis an angle of

1. ${45}^{\circ }$
2. ${60}^{\circ }$
3. $0^{\circ }$
4. ${30}^{\circ }$