# 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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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 |
57%
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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 $\stackrel{\to }{\mathrm{r}}$ $=$ $\left(\mathrm{a}\right)$ $\mathrm{sin}$ $\mathrm{\omega t}\stackrel{^}{\mathrm{i}}$ $+$ $\left(\mathrm{a}\right)$ $\mathrm{cos}$ $\mathrm{\omega t}\stackrel{^}{\mathrm{j}}$. The velocity of the particle is:

 1 parallel to the position vector. 2 at 60° 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 ${\mathrm{v}}_{0}$ 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.  $\sqrt{3}{\mathrm{v}}_{0}$ $\mathrm{cos\theta }$

2.  $\frac{{\mathrm{v}}_{0}}{\sqrt{2}}\mathrm{sin}$ $\mathrm{\theta }$

3.  $\frac{{\mathrm{v}}_{0}}{\sqrt{2}}\mathrm{cos}\theta$

4.  $\sqrt{5}{\mathrm{v}}_{0}$

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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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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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.  $\frac{\sqrt{3}}{2}$

Subtopic:  Speed & Velocity |
62%
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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 |
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