# The position vector of a particle is $$\vec{r}= a \sin\omega t \hat{i} + a\cos \omega t \hat{j}$$. The velocity of the particle is: 1.  parallel to the position vector. 2.  at $$60^{\circ}$$ with position vector. 3.  parallel to the acceleration vector. 4.  perpendicular to the position vector.

Subtopic:  Circular Motion |
80%
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A projectile is projected from the ground with the velocity $$v_{0}$$ at an angle $$\theta$$ with the horizontal. What is the vertical component of the velocity of the projectile when its vertical displacement is equal to half of the maximum height attained?
1. $$\sqrt{3} v_{0}\cos\theta$$
2. $$\frac{v_{0}}{\sqrt{2}} \sin\theta$$
3. $$\frac{v_{0}}{\sqrt{2}} \cos \theta$$

4. $$\sqrt{5} v_{0}$$

Subtopic:  Projectile Motion |
70%
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A particle starts moving on a circular path from rest, such that its tangential acceleration varies with time as $$a_t=kt$$. Distance traveled by particle on the circular path in time $$t$$ is:
1. $$\frac{kt^3}{3}$$
2. $$\frac{kt^2}{6}$$
3. $$\frac{kt^3}{6}$$
4. $$\frac{k t^2}{2}$$

Subtopic:  Circular Motion |
72%
From NCERT
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The speed of water in a river is $$4$$ km/h and a man can swim at $$5$$ km/h. The minimum time taken by the man to cross the river of width $$200$$ m is:
1. $$\frac{1}{5}~\text{h}$$
2. $$\frac{1}{25}~\text{h}$$
3. $$\frac{1}{15}~\text{h}$$
4. $$\frac{1}{20}~\text{h}$$

Subtopic:  Relative Motion |
57%
From NCERT
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A particle is moving on a circular path of radius $$R.$$ When the particle moves from point $$A$$ to $$B$$ (angle $$\theta$$), the ratio of the distance to that of the magnitude of the displacement will be:

 1 $\frac{\mathrm{\theta }}{\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 2 $\frac{\mathrm{\theta }}{2\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 3 $\frac{\mathrm{\theta }}{2\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 4 $\frac{\mathrm{\theta }}{\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 
Subtopic:  Position & Displacement |
75%
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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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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 |
62%
From NCERT
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A particle is moving along a curve. Select the correct statement.

 1 If its speed is constant, then it has no acceleration. 2 If its speed is increasing, then the acceleration of the particle is along its direction of motion. 3 If its speed is decreasing, then the acceleration of the particle is opposite to its direction of motion. 4 If its speed is constant, its acceleration is perpendicular to its velocity.
Subtopic:  Acceleration |
69%
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A car is moving along east at $$10$$ m/s and a bus is moving along north at $$10$$ m/s. The velocity of the car with respect to the bus is along:

 1 North-East 2 South-East 3 North-West 4 South-West
Subtopic:  Relative Motion |
60%
From NCERT
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A particle starts moving from the origin in the XY plane and its velocity after time $$t$$ is given by $$\overrightarrow{{v}}=4 \hat{{i}}+2 {t} \hat{{j}}$$. The trajectory of the particle is correctly shown in the figure:

 1 2 3 4
Subtopic:  Speed & Velocity |
61%
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