# 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 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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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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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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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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A body is projected with velocity $$\vec{v} = \left( \alpha \hat{i} + \beta \hat{j} \right)~\text{m/s}$$. The time of flight of the body is: [considering $$x$$ as horizontal and $$y$$ as vertical axis and $$g$$ is acceleration due to gravity]
1. $$\frac{2 \beta}{g}$$
2. $$\frac{2 \alpha}{g}$$
3. $$\frac{2 \alpha \beta}{g}$$
4. $$\frac{2 \alpha}{g \beta}$$
Subtopic:  Projectile Motion |
77%
From NCERT
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A car moves on a circular path such that its speed is given by $$v= Kt$$, where $$K$$ = constant and $$t$$ is time. Also given: radius of the circular path is $$r$$. The net acceleration of the car at time $$t$$ will be:
1. $$\sqrt{K^{2} +\left(\frac{K^{2} t^{2}}{r}\right)^{2}}$$
2. $$2K$$
3. $$K$$
4. $$\sqrt{K^{2} + K^{2} t^{2}}$$

Subtopic:  Circular Motion |
80%
From NCERT
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Raindrops are falling with speed $$v$$ vertically downwards and a man is running on a horizontal road with speed $$u.$$ The magnitude of the velocity of the raindrops with respect to the man is:
1. $$v-u$$
2. $$v+u$$
3. $$\sqrt{{v}^2 + {u}^2 \over 2}$$
4. $$\sqrt{{v}^2 + {u}^2}$$

Subtopic:  Relative Motion |
82%
From NCERT
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The equation of trajectory of a projectile is given by $$y = x-10x^{2}$$Its speed of projection is: ($$g =1 0$$ m/${\mathrm{s}}^{2}$)
1. $$1$$ m/s

2. $$2$$ m/s

3. $$3$$ m/s

4. $$4$$ m/s

Subtopic:  Projectile Motion |
73%
From NCERT
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A particle is thrown obliquely at $$t=0$$. The particle has the same K.E. at $$t=5$$ seconds and at $$t=9$$ seconds. The particle attains maximum altitude at:
1. $$t=6$$ s
2. $$t=7$$ s
3. $$t=8$$ s
4. $$t=14$$ s

Subtopic:  Projectile Motion |
75%
From NCERT
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