# 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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Three balls are thrown from the top of a building with equal speeds at different angles. When the balls strike the ground, their speeds are $$v_{1} , v_{2}$$ $$\text{and}$$ $$v_{3}$$ respectively, then:

1. $$v_{1} > v_{2} > v_{3}$$
2. $$v_{3} > v_{2} = v_{1}$$
3. $$v_{1} = v_{2} = v_{3}$$
4. $$v_{1} < v_{2} < v_{3}$$${}_{}$

Subtopic:  Projectile Motion |
74%
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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A body is moving with a velocity of $$30$$ m/s towards the east. After $$10$$ s, its velocity becomes $$40$$ m/s towards the north. The average acceleration of the body is:
1. $$7~\text{m/s}^2$$
2. $$\sqrt{7}~\text{m/s}^2$$
3. $$5~\text{m/s}^2$$
4. $$1~\text{m/s}^2$$

Subtopic:  Acceleration |
77%
From NCERT
AIPMT - 2011
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The velocity of a projectile at the initial point $$A$$ is $$2\hat i+3\hat j~$$m/s. Its velocity (in m/s) at point $$B$$ is:

 1 $$-2\hat i+3\hat j~$$ 2 $$2\hat i-3\hat j~$$ 3 $$2\hat i+3\hat j~$$ 4 $$-2\hat i-3\hat j~$$
Subtopic:  Projectile Motion |
83%
From NCERT
AIPMT - 2013
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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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Certain neutron stars are believed to be rotating at about $$1$$ rev/s. If such a star has a radius of $$20$$ km, the acceleration of an object on the equator of the star will be:

 1 $$20 \times 10^8 ~\text{m/s}^2$$ 2 $$8 \times 10^5 ~\text{m/s}^2$$ 3 $$120 \times 10^5 ~\text{m/s}^2$$ 4 $$4 \times 10^8 ~\text{m/s}^2$$
Subtopic:  Circular Motion |
70%
From NCERT
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The angle turned by a body undergoing circular motion depends on the time as given by the equation, $$\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}$$. It can be deduced that the angular acceleration of the body is?
1. $$\theta_1$$
2. $$\theta_2$$
3. $$2\theta_1$$
4. $$2\theta_2$$

Subtopic:  Circular Motion |
84%
From NCERT
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A vector $\stackrel{\to }{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $|\Delta \stackrel{\to }{a}|$ and $\Delta a$ are, respectively:

 1 $$0, ad\theta$$ 2 $$a d\theta, 0$$ 3 $$0,0$$ 4 None of these
Subtopic:  Position & Displacement |
53%
From NCERT
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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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