# If a particle is moving in a circular orbit with constant speed, then: 1. its velocity is variable. 2. its acceleration is variable. 3. its angular momentum is constant. 4. All of the above

Subtopic:  Circular Motion |
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A projectile is projected with initial kinetic energy $$K$$. If it has kinetic energy $$0.25K$$ at its highest point, then the angle of projection is:
1. $$30^{\circ}$$
2. $$45^{\circ}$$
3. $$60^{\circ}$$
4. $$75^{\circ}$$

Subtopic:  Projectile Motion |
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If the position of a particle varies according to the equations $$x= 3t^2$$${}^{}$, $$y =2t$$, and $$z= 4t+4$$, then which of the following is incorrect?

 1 Velocities in $$y$$ and $$z$$ directions are constant 2 Acceleration in the $$x\text-$$direction is non-uniform 3 Acceleration in the $$x\text-$$direction is uniform 4 Motion is not in a straight line
Subtopic:  Acceleration |
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If three coordinates of a particle change according to the equations $$x = 3 t^{2}, y = 2 t , z= 4$$, then the magnitude of the velocity of the particle at time $$t=1$$ second will be:
1. $$2\sqrt{11}~\text{unit}$$
2. $$\sqrt{34}~\text{unit}$$

3. $$40~\text{unit}$$
4. $$2\sqrt{10}~\text{unit}$$

Subtopic:  Speed & Velocity |
81%
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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 |
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