# Coordinates of a particle as a function of time $$t$$ are $$x= 2t$$, $$y =4t$$. It can be inferred that the path of the particle will be: 1. Straight line 2. Ellipse 3. Parabola 4. Hyperbola

Subtopic:  Position & Displacement |
75%
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When a man walks on a horizontal road with velocity $$1$$ km/h, the rain appears to him coming vertically at a speed of $$2$$ km/h. The actual speed of the rain with respect to ground is:
1. $$\sqrt{3}$$ km/h
2. $$\sqrt{5}$$ km/h
3. $$1$$ km/h
4. $$3$$ km/h

Subtopic:  Relative Motion |
72%
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Which of the following statement/s is/are incorrect regarding the motion in a plane?

 1 a body can't move on a curved path with constant acceleration. 2 the angle between acceleration and velocity can be $$90^\circ.$$ 3 the angle between acceleration and velocity can be other than $$90^\circ.$$ 4 all of the above.
Subtopic:  Circular Motion |
58%
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A body started moving with an initial velocity of $$4$$ m/s along the east and an acceleration $$1$$ m/s2 along the north. The velocity of the body just after $$4$$ s will be?

 1 $$8$$ m/s along East. 2 $$4 \sqrt{2}$$ m/s along North-East. 3 $$8$$ m/s along North. 4 $$4 \sqrt{2}$$ m/s along South-East.
Subtopic:  Uniformly Accelerated Motion |
78%
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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 |
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The position vector of a particle is $$\overrightarrow{r}= a \sin\omega t\hat i + a\cos \omega t\hat j$$. 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 |
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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 |
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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 |
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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%
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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 |
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