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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The position of a moving particle at time $$t$$ is $$\vec{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.$$ Its displacement during the time interval $$t=1$$ s to $$t=3$$ s will be:

 1 $$\hat{j}-\hat{k}$$ 2 $$3\hat{i}-4\hat{j}-\hat{k}$$ 3 $$9\hat{i}+36\hat{j}-27\hat{k}$$ 4 $$32\hat{j}-26\hat{k}$$
Subtopic:  Position & Displacement |
80%
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 particle starting from the point $$(1,2)$$ moves in a straight line in the XY-plane. Its coordinates at a later time are $$(2,3).$$ The path of the particle makes with x-axis an angle of:

 1 $$30^\circ$$ 2 $$45^\circ$$ 3 $$60^\circ$$ 4 data is insufficient
Subtopic:  Position & Displacement |
80%
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 starting from the origin $$(0,0)$$ moves in a straight line in the $$(x,y)$$ plane. Its coordinates at a later time are ($\sqrt{3}$, $$3$$). The path of the particle makes an angle of __________ with the x-axis:
1. $$30^\circ$$
2. $$45^\circ$$
3. $$60^\circ$$
4. $$0$$

Subtopic:  Position & Displacement |
76%
From NCERT
AIPMT - 2007
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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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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 |
74%
From NCERT
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An aeroplane flies $$400$$ m north and then $$300$$west and then flies $$1200$$ m upwards. Its net displacement is:

 1 $$1200$$ m 2 $$1300$$ m 3 $$1400$$ m 4 $$1500$$ m

Subtopic:  Position & Displacement |
73%
From NCERT
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A body starts moving from rest on a horizontal ground such that the position vector of the body with respect to its starting point is given by $\mathrm{r}$ $=$ $2\mathrm{t}\stackrel{^}{\mathrm{i}}$ $+$ $3{\mathrm{t}}^{2}\stackrel{^}{\mathrm{j}}$. The equation of the trajectory of the body is:

1. y = 1.5 x

2. y = 0.75 ${\mathrm{x}}^{2}$

3. y = 1.5 ${\mathrm{x}}^{2}$

4. y = 0.45 ${\mathrm{x}}^{2}$

Subtopic:  Position & Displacement |
66%
From NCERT
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