Consider the motion of the tip of the second hand of a clock. In one minute (assuming $$R$$ to be the length of the second hand), its:

 1 displacement is $$2\pi R$$ 2 distance covered is $$2R$$ 3 displacement is zero. 4 distance covered is zero.
Subtopic:  Position & Displacement |
86%
From NCERT
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Three girls skating on a circular ice ground of radius $$200$$ m start from a point $$P$$ on the edge of the ground and reach a point $$Q$$ diametrically opposite to $$P$$ following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

1.  $A>B>C$

2. $C>A>B$

3. $B>A>C$

4. $A=B=C$

Subtopic:  Position & Displacement |
84%
From NCERT
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A cat is situated at point $$A$$ ($$0,3,4$$) and a rat is situated at point $$B$$ ($$5,3,-8$$). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. 5 unit
2. 12 unit
3. 13 unit
4. 17 unit

Subtopic:  Position & Displacement |
74%
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 |
74%
From NCERT
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A vector $\stackrel{\to }{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $|\Delta \stackrel{\to }{a}|$ and $\Delta a$ are, respectively:

 1 0, adθ 2 dθ, 0 3 0, 0 4 None of these
Subtopic:  Position & Displacement |
54%
From NCERT
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A particle is moving such that its position coordinates $$(x,y)$$ are $$(2$$ m, $$3$$ m) at time $$t=0,$$ $$(6$$ m, $$7$$ m) at time $$t=2$$ s and $$(13$$ m, $$14$$ m) at time $$t=5$$ s. Average velocity vector $$(v_{avg})$$ from $$t=0$$ to $$t=5$$ s is:

 1 $$\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )$$ 2 $$\frac{7}{3}\left ( \hat{i}+\hat{j} \right )$$ 3 $$2\left ( \hat{i}+\hat{j} \right )$$ 4 $$\frac{11}{5}\left ( \hat{i}+\hat{j} \right )$$
Subtopic:  Speed & Velocity |
81%
From NCERT
NEET - 2014
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A car turns at a constant speed on a circular track of radius $$100$$ m, taking $$62.8$$ s for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

 1 $$0,~0$$ 2 $$0,~10$$ m/s 3 $$10$$ m/s, $$10$$ m/s 4 $$10$$ m/s, $$0$$
Subtopic:  Speed & Velocity |
82%
From NCERT
AIPMT - 2006
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The coordinates of a moving particle at any time ‘t’ are given by x = αt3 and y = βt3. The speed of the particle at time ‘t’ is given by:

1. $\sqrt{{\alpha }^{2}+{\beta }^{2}}$

2. $3$ $t\sqrt{{\alpha }^{2}+{\beta }^{2}}$

3. $3$ ${t}^{2}\sqrt{{\alpha }^{2}+{\beta }^{2}}$

4. ${t}^{2}\sqrt{{\alpha }^{2}+{\beta }^{2}}$

Subtopic:  Speed & Velocity |
78%
From NCERT
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Two particles A and B, move with constant velocities $$\vec{v_1}$$   and  $$\vec{v_2}$$ . At the initial moment their position vector are  $$\vec{r_1}$$ and  $$\vec{r_2}$$  respectively. The condition for particles A and B for their collision to happen will be:

1.

2.

3.

4.

Subtopic:  Speed & Velocity |
71%
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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%
From NCERT
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