A particle is moving such that its position coordinates $$(x,y)$$ are $$(2$$ m, $$3$$ m) at time $$t=0,$$ $$(6$$ m, $$7$$ m) at time $$t=2$$ s and $$(13$$ m, $$14$$ m) at time $$t=5$$ s. Average velocity vector $$(v_{avg})$$ from $$t=0$$ to $$t=5$$ s is:

 1 $$\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )$$ 2 $$\frac{7}{3}\left ( \hat{i}+\hat{j} \right )$$ 3 $$2\left ( \hat{i}+\hat{j} \right )$$ 4 $$\frac{11}{5}\left ( \hat{i}+\hat{j} \right )$$
Subtopic:  Speed & Velocity |
81%
From NCERT
NEET - 2014
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If three coordinates of a particle change according to the equations $$x = 3 t^{2}, y = 2 t , z= 4$$, then the magnitude of the velocity of the particle at time $$t=1$$ second will be:
1. $$2\sqrt{11}~\text{unit}$$
2. $$\sqrt{34}~\text{unit}$$

3. $$40~\text{unit}$$
4. $$2\sqrt{10}~\text{unit}$$

Subtopic:  Speed & Velocity |
80%
From NCERT
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A car turns at a constant speed on a circular track of radius $$100$$ m, taking $$62.8$$ s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

 1 $$0,~0$$ 2 $$0,~10$$ m/s 3 $$10$$ m/s, $$10$$ m/s 4 $$10$$ m/s, $$0$$
Subtopic:  Speed & Velocity |
82%
From NCERT
AIPMT - 2006
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The coordinates of a moving particle at any time $$t$$ are given by $$x= \alpha t^3$$ and $$y = \beta t^3$$. The speed of the particle at time $$t$$ is given by:

 1 $$\sqrt{\alpha^{2} + \beta^{2}}$$ 2 $$3t \sqrt{\alpha^{2} + \beta^{2}}$$ 3 $$3t^{2} \sqrt{\alpha^{2} +\beta^{2}}$$ 4 $$t^{2} \sqrt{\alpha^{2} +\beta^{2}}$$
Subtopic:  Speed & Velocity |
78%
From NCERT
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A particle moves along the positive branch of the curve $$y= \frac{x^{2}}{2}$$ where $$x= \frac{t^{2}}{2}$$, & $$x$$ and $$y$$ are measured in metres and in seconds respectively. At $$t= 2~\text{s}$$, the velocity of the particle will be:
1. $$\left(\right. 2 \hat{i} - 4 \hat{j})~\text{m/s}$$
2. $$\left(\right. 4 \hat{i} + 2 \hat{j}\left.\right)\text{m/s}$$
3. $$\left(\right. 2 \hat{i} + 4 \hat{j}\left.\right) \text{m/s}$$
4. $$\left(\right. 4 \hat{i} - 2 \hat{j}\left.\right) \text{m/s}$$

Subtopic:  Speed & Velocity |
73%
From NCERT
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In $$1.0~\text{s}$$, a particle goes from point $$A$$ to point $$B$$, moving in a semicircle of radius $$1.0~\text{m}$$ (see figure). The magnitude of the average velocity is:

 1 $$3.14~\text{m/s}$$ 2 $$2.0~\text{m/s}$$ 3 $$1.0~\text{m/s}$$ 4 zero
Subtopic:  Speed & Velocity |
76%
From NCERT
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Two particles $$A$$ and $$B$$, move with constant velocities $$\overrightarrow{v_1}$$ and $$\overrightarrow{v_2}$$. At the initial moment their position vector are $$\overrightarrow {r_1}$$ and $$\overrightarrow {r_2}$$ respectively. The condition for particles $$A$$ and $$B$$ for their collision to happen will be:
1. $$\overrightarrow{r_{1 }} . \overrightarrow{v_{1}} = \overrightarrow{r_{2 }} . \overrightarrow{v_{2}}$$
2. $$\overrightarrow{r_{1}} \times\overrightarrow{v_{1}} = \overrightarrow{r_{2}} \times \overrightarrow {v_{2}}$$
3. $$\overrightarrow{r_{1}}-\overrightarrow{r_{2}}=\overrightarrow{v_{1}} - \overrightarrow{v_{2}}$$
4. $$\frac{\overrightarrow{r_{1}} - \overrightarrow{r_{2}}}{\left|\overrightarrow{r_{1}} - \overrightarrow{r_{2}}\right|} = \frac{\overrightarrow{v_{2}} - \overrightarrow{v_{1}}}{\left|\overrightarrow{v_{2}} - \overrightarrow{v_{1}}\right|}$$

Subtopic:  Speed & Velocity |
71%
From NCERT
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Two particles move from $$A$$ to $$C$$ and $$A$$ to $$D$$ on a circle of radius $$R$$ and diameter $$AB$$. If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is:

1. $$2$$
2. $$2\sqrt{3}$$

3. $$\sqrt{3}$$
4. $$\frac{\sqrt{3}}{2}$$

Subtopic:  Speed & Velocity |
63%
From NCERT
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A particle moves on the curve ${\mathrm{}}^{}$$$x^2 = 2y$$$\mathrm{}$. The angle of its velocity vector with the $$x$$-axis at the point $$\left(1, \frac{1}{2}\right )$$ will be:

 1 $$30^\circ$$ 2 $$60^\circ$$ 3 $$45^\circ$$ 4 $$75^\circ$$
Subtopic:  Speed & Velocity |
61%
From NCERT
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The position of a particle is given by;
$$\overrightarrow{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})$$ m $\stackrel{}{\mathrm{}}$
where $$t$$ is in seconds and the coefficients have the proper units for $$r$$ to be in meters. The magnitude and direction of $$\overrightarrow{v}(t)$$ at $$t=1.0$$ s are:

 1 $$4$$ m/s $$53^\circ$$ with $$x$$-axis 2 $$4$$  m/s $$37^\circ$$ with $$x$$-axis 3 $$5$$ m/s $$53^\circ$$ with $$y$$-axis 4 $$5$$  m/s $$53^\circ$$ with $$x$$-axis
Subtopic:  Speed & Velocity |
66%
From NCERT
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