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 |
 81%
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 (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. θsinθ2

2. θ2sinθ2

3. θ2cosθ2

4. θcosθ2

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 r = 2ti^ + 3t2j^. The equation of the trajectory of the body is:

1. y = 1.5 x

2. y = 0.75 x2

3. y = 1.5 x2

4. y = 0.45 x2

Subtopic:  Position & Displacement |
 67%
From NCERT
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