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Q. No.The position vector of a particle changes with time according to the relation,
\(\vec{r}(t)=(15 t^2) \hat{i}+\left(4-20 t^2\right) \hat{j},\) where \(\vec{r}(t)\) is in metres and \(t\) is in seconds.
What is the magnitude of the acceleration at \(t=1\) second?
\(\vec{r}(t)=(15 t^2) \hat{i}+\left(4-20 t^2\right) \hat{j},\) where \(\vec{r}(t)\) is in metres and \(t\) is in seconds.
What is the magnitude of the acceleration at \(t=1\) second?
| 1. | \(100\) m/s2 | 2. | \(40\) m/s2 |
| 3. | \(50\) m/s2 | 4. | \(25\) m/s2 |
Subtopic: Acceleration |
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Level 1: 80%+
JEE
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The position vector of a particle is expressed as: \(\overrightarrow{r}\left({t}\right){=}({8}{t}\hat{i}{+}{5}{t}^{2}\hat{j}{+}{6}\hat{k}).\) Which of the following statements correctly describes the direction of the particle’s acceleration?
| 1. | It is directed along the positive \({y \text-}\)axis. |
| 2. | It is directed along the positive \({x \text-}\)axis. |
| 3. | It is equally inclined to the \(x\) and \({y \text-}\)axis. |
| 4. | It is directed along the positive \({z \text-}\)axis. |
Subtopic: Acceleration |
74%
Level 2: 60%+
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A particle moves such that its position vector \(\vec{r}(t)=\cos \omega t \hat{i}+\sin \omega t \hat{j},\) where \(\omega\) is a constant and \(t\) is time. Then which of the following statements is true for the velocity \(\vec{{v}}({t})\) and acceleration \(\vec{a}(t)\) of the particle:
| 1. | \(\vec{v}\) is perpendicular to \(\vec{r}\) and \(\vec{a}\) is directed towards the origin. |
| 2. | \(\vec{v}\) and \(\vec{a}\) both are parallel to \(\vec{r}\) |
| 3. | \(\vec{v}\) is perpendicular to \(\vec{r}\) and \(\vec{a}\) is directed away from the origin. |
| 4. | \(\vec{v}\) and \(\vec{a}\) both are perpendicular to \(\vec{r}\) |
Subtopic: Acceleration |
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The velocity-displacement graph describing the motion of a bicycle is shown in the figure. The acceleration displacement graph of the bicycle’s motion is best described by:
| 1. |  |
3. |  |
| 2. |  |
4. |  |
Subtopic: Acceleration |
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A mosquito is moving with a velocity \(\vec{v}=0.5 t^2 \hat{i}+3 t \hat{j}+9 \hat{k}~\text{m/s},\) and accelerating in uniform conditions. What will be the direction of mosquitoes after \(2~\text{s}?\)
| 1. | \(\tan ^{-1}\left(\frac{2}{3}\right) \) from \(x\text-\)axis |
| 2. | \(\tan ^{-1}\left(\frac{5}{2}\right) \) from \(x\text-\)axis |
| 3. | \(\tan ^{-1}\left(\frac{5}{2}\right) \) from \(y\text-\)axis |
| 4. | \(\tan ^{-1}\left(\frac{2}{3}\right) \) from \(y\text-\)axis |
Subtopic: Acceleration |
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At time \(t=0,\) a particle starts travelling from a height of \(7\hat z\) cm in a plane, keeping the \(\mathrm{z}\)-coordinate constant. At any instant of time, its position along the \(x\text-\) and \(y\text-\)directions is defined as \(3t\) and \(5t^{3}\) respectively. At \(t=1 \) s, the acceleration of the particle is:
1. \(-30\hat{y} \)
2. \(30\hat{y}\)
3. \(3\hat{x} +15\hat{y} \)
4. \(3\hat{x} + 15\hat{y} + 7\hat{z}\)
1. \(-30\hat{y} \)
2. \(30\hat{y}\)
3. \(3\hat{x} +15\hat{y} \)
4. \(3\hat{x} + 15\hat{y} + 7\hat{z}\)
Subtopic: Acceleration |
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Level 2: 60%+
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At \(t = 0,\) a body of mass \(100~\text{g}\) starts moving under the influence of a force \((5\hat{i}+ 10\hat{j})~\text{N}.\) After \(2~\text{s}\) its position is \((2x\hat{i}+5y\hat{j})~\text{m}.\)
The ratio \(x : y\) is:
1. \(1:2\)
2. \(2:5\)
3. \(5:2\)
4. \(5:4\)
The ratio \(x : y\) is:
1. \(1:2\)
2. \(2:5\)
3. \(5:2\)
4. \(5:4\)
Subtopic: Acceleration |
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The velocity of particle is given as \(\vec{v}=-x \hat{i}+2 y \hat{j}-z \hat{k} ~\text{m/s}.\) The magnitude of acceleration at point \((1,2,4)\) is: (in \(\text{m/s}^2\))
1. \(\sqrt{6}\)
2. \(9\)
3. \(\sqrt{33}\)
4. \(0\)
1. \(\sqrt{6}\)
2. \(9\)
3. \(\sqrt{33}\)
4. \(0\)
Subtopic: Acceleration |
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