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 $2\pi \mathrm{R.}$

2. distance covered is 2R.

3. displacement is zero.

4. distance covered is zero.

Subtopic:  Position & Displacement |
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The position of a moving particle at time t is $\stackrel{\to }{\mathrm{r}}=3\stackrel{^}{\mathrm{i}}+4{\mathrm{t}}^{2}\stackrel{^}{\mathrm{j}}-{\mathrm{t}}^{3}\stackrel{^}{\mathrm{k}}$. Its displacement during the time interval t = 1 sec to t = 3 sec will be

1. $\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{k}}$

2. $3\stackrel{^}{\mathrm{i}}-4\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{k}}$

3. $9\stackrel{^}{\mathrm{i}}+36\stackrel{^}{\mathrm{j}}-27\stackrel{^}{\mathrm{k}}$

4. $32\stackrel{^}{\mathrm{j}}-26\stackrel{^}{\mathrm{k}}$

Subtopic:  Position & Displacement |
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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 |
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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 the x-axis, an angle of

1. 30°

2. 45°

3. 60°

4. data insufficient

Subtopic:  Position & Displacement |
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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 traveled by the cat to catch the rat is:

1. 5 unit

2. 12 unit

3. 13 unit

4. 17 unit

Subtopic:  Position & Displacement |
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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. 30o

2. 45o

3. 60o

4. 0o

Subtopic:  Position & Displacement |
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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 $\mathrm{\theta }$), 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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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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An aeroplane flies 400 m north and then 300 m 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 |
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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 . 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 |
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