# In a uniform circular motion, if the speed of the particle is $$2$$ m/s and radius of the circle is $$2$$ m, then the values of centripetal and tangential acceleration are, respectively: 1. $$2~\text{m/s}^2,~2~\text{m/s}^2$$ 2. $$2~\text{m/s}^2,~1~\text{m/s}^2$$ 3. $$0,~2~\text{m/s}^2$$ 4. $$2~\text{m/s}^2,~0$$

Subtopic:  Circular Motion |
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A person, who can swim with speed $$u$$ relative to water, wants to cross a river (of width $$d$$ and water is flowing with speed $$v$$). The minimum time in which the person can do so is:
1. $$\frac{d}{v}$$
2. $$\frac{d}{u}$$
3. $$\frac{d}{\sqrt{v^{2} + u^{2}}}$$
4. $$\frac{d}{\sqrt{v^{2} - u^{2}}}$$

Subtopic:  Relative Motion |
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The position vector of a particle $$\overrightarrow r$$ as a function of time $$t$$ (in seconds) is $$\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}$$. The initial acceleration of the particle is:
1. $$2~\text{m/s}^2$$
2. $$3~\text{m/s}^2$$
3. $$4~\text{m/s}^2$$

4. zero

Subtopic:  Acceleration |
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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 |
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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 |
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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 |
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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 $$\vec{r}= a \sin\omega t \hat{i} + a\cos \omega t \hat{j}$$. 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 |
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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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