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 |
82%
From NCERT
NEET - 2014
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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 |
79%
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. $$\dfrac{\sqrt{3}}{2}$$

Subtopic:  Speed & Velocity |
63%
From NCERT
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The position of a particle is given by;
$$\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})$$ m where $$t$$ is in seconds and the coefficients have the proper units for $$r$$ to be in metres. The magnitude and direction of $$\vec{v}(t)$$ 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 |
68%
From NCERT
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A bus is going to the North at a speed of $$30$$ kmph. It makes a $$90^{\circ}$$ left turn without changing the speed. The change in the velocity of the bus is:

 1 $$30$$ kmph towards $$W$$ 2 $$30$$ kmph towards $$S\text-W$$ 3 $$42.4$$ kmph towards $$S\text-W$$ 4 $$42.4$$ kmph towards $$N\text-W$$
Subtopic:  Speed & Velocity |
58%
From NCERT
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Three particles are moving with constant velocities $$v_1 ,v_2$$ and $$v$$ respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among $$v_1 ,v_2$$ and $$v$$ is:

1. $$v =v_1+v_2$$
2. $$v= \sqrt{v_{1} v_{2}}$$
3. $$v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}$$
4. $$v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}$$

Subtopic:  Speed & Velocity |
53%
From NCERT
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