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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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 |
 80%
From NCERT
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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 \(x= \alpha t^3\) and \(y = \beta t^3\). The speed of the particle at 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 |
 78%
From NCERT
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A particle moves along the positive branch of the curve \(y= \frac{x^{2}}{2}\) where \(x= \frac{t^{2}}{2}\), & \(x\) and \(y\) are measured in metres and in seconds respectively. At \(t= 2~\text{s}\), the velocity of the particle will be:
1. \(\left(\right. 2 \hat{i} - 4 \hat{j})~\text{m/s}\) 
2. \(\left(\right. 4 \hat{i} + 2 \hat{j}\left.\right)\text{m/s}\)
3. \(\left(\right. 2 \hat{i} + 4 \hat{j}\left.\right) \text{m/s}\)
4. \(\left(\right. 4 \hat{i} - 2 \hat{j}\left.\right) \text{m/s}\)

Subtopic:  Speed & Velocity |
 73%
From NCERT
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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 |
 76%
From NCERT
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Two particles \(A\) and \(B\), move with constant velocities \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\). At the initial moment their position vector are \(\overrightarrow {r_1}\) and \(\overrightarrow {r_2}\) respectively. The condition for particles \(A\) and \(B\) for their collision to happen will be:
1. \(\overrightarrow{r_{1  }} . \overrightarrow{v_{1}}   = \overrightarrow{r_{2  }} . \overrightarrow{v_{2}}\)
2. \(\overrightarrow{r_{1}} \times\overrightarrow{v_{1}}   = \overrightarrow{r_{2}} \times \overrightarrow {v_{2}}\)
3. \(\overrightarrow{r_{1}}-\overrightarrow{r_{2}}=\overrightarrow{v_{1}} - \overrightarrow{v_{2}}\)
4. \(\frac{\overrightarrow{r_{1}} - \overrightarrow{r_{2}}}{\left|\overrightarrow{r_{1}} -  \overrightarrow{r_{2}}\right|} =   \frac{\overrightarrow{v_{2}} -  \overrightarrow{v_{1}}}{\left|\overrightarrow{v_{2}} -   \overrightarrow{v_{1}}\right|}\)

Subtopic:  Speed & Velocity |
 71%
From NCERT
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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 |
 63%
From NCERT
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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 |
 61%
From NCERT
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The position of a particle is given by;
\(\overrightarrow{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m 
where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\overrightarrow{v}(t)\) at \(t=1.0\) s are:

1. \(4\) m/s \(53^\circ\) with \(x\)-axis
2. \(4\) m/s \(37^\circ\) with \(x\)-axis
3. \(5\) m/s \(53^\circ\) with \(y\)-axis
4. \(5\) m/s \(53^\circ\) with \(x\)-axis
Subtopic:  Speed & Velocity |
 66%
From NCERT
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