A particle is moving with veocity v=k(yi^+xj^); where k is constant. The general equation for the path is:

1. y=x2+constant

2. y2=x2+constant

3. y=x+constant

4. xy=constant

 

Subtopic:  Speed & Velocity |
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In \(1.0~\text{s}\), a particle goes from point \(A\) to point \(B\), moving in a semicircle of radius \(1.0~\text{m}\) (see figure). The magnitude of the average velocity is:

          
1. \(3.14~\text{m/s}\)
2. \(2.0~\text{m/s}\)
3. \(1.0~\text{m/s}\)
4. zero

Subtopic:  Speed & Velocity |
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The coordinates of a moving particle at any time \(t\) are given by \(x= \alpha t^3\) and \(y = \beta t^3.\) The speed of the particle at a time \(t\) is given by:

1. \(\sqrt{\alpha^{2} + \beta^{2}}\) 2. \(3t \sqrt{\alpha^{2} + \beta^{2}}\)
3. \(3t^{2} \sqrt{\alpha^{2} +\beta^{2}}\) 4. \(t^{2} \sqrt{\alpha^{2} +\beta^{2}}\)
Subtopic:  Speed & Velocity |
 80%
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A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2s and (13m, 14m) at time t = 5s. Average velocity vector (vav) from t = 0 to t = 5s is

1. 15(13i^+14j^)

2. 73(i^+j^)

3. 2(i^+j^)

4. 115(i^+j^)

Subtopic:  Speed & Velocity |
 80%
From NCERT
NEET - 2014
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The coordinates of a moving particle at a time t, are given by, x = 5sin10t, y = 5cos10t. The speed of the particle is:

(1)  25

(2)  50

(3)  10

(4)  502

Subtopic:  Speed & Velocity |
 50%
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A car turns at a constant speed on a circular track of radius \(100~\text m,\) taking \(62.8~\text s\) for every circular lap. The average velocity and average speed for each circular lap, respectively, is:

1. \(0,~0\) 2. \(0,\)  \(10~\text{m/s},\)
3. \(10~\text{m/s},\) ​​​​​​​ \(10~\text{m/s},\) 4. \(10~\text{m/s},\) \(0\)
Subtopic:  Speed & Velocity |
 83%
From NCERT
AIPMT - 2006
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If three coordinates of a particle change according to the equations \(x = 3 t^{2}, y = 2 t , z= 4\), then the magnitude of the velocity of the particle at time \(t=1\) second will be:
1. \(2\sqrt{11}~\text{unit}\)
2. \(\sqrt{34}~\text{unit}\)

3. \(40~\text{unit}\)
4. \(2\sqrt{10}~\text{unit}\)

Subtopic:  Speed & Velocity |
 82%
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Two particles move from \(A\) to \(C\) and \(A\) to \(D\) on a circle of radius \(R\) and the diameter \(AB.\) If the time taken by both particles is the same, then the ratio of magnitudes of their average velocities is:
                                
1. \(2\)
2. \(2\sqrt{3}\)

3. \(\sqrt{3}\)
4. \(\dfrac{\sqrt{3}}{2}\)

Subtopic:  Speed & Velocity |
 63%
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A particle moves on the curve \(x^2 = 2y\). 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 |
 63%
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A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{{v}}=4 \hat{{i}}+2 {t} \hat{{j}}\). The trajectory of the particle is correctly shown in the figure:

1. 2.
3. 4.
Subtopic:  Speed & Velocity |
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