A particle initially at rest starts moving from reference point. $\mathrm{x}=0$ along $\mathrm{x}$-axis, with velocity $v$ that varies as $v=4 \sqrt{\mathrm{x} m} / \mathrm{s}$. The acceleration of the particle is __________$ \mathrm{ms}^{-2}$.
A particle initially at rest starts moving from reference point. $\mathrm{x}=0$ along $\mathrm{x}$-axis, with velocity $v$ that varies as $v=4 \sqrt{\mathrm{x} m} / \mathrm{s}$. The acceleration of the particle is __________$ \mathrm{ms}^{-2}$.
- [JEE MAIN 2024]
- A
$7$
- B
$8$
- C
$9$
- D
$10$
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- [AIIMS 2002]
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For the velocity-time graph shown in the figure, in a time interval from $t=0$ to $t=6\,s$, match the following columns.
Colum $I$
Colum $II$
$(A)$ Change in velocity
$(p)$ $-5 / 3\,Sl$ unit
$(B)$ Average acceleration
$(q)$ $-20\,SI$ unit
$(C)$ Total displacement
$(r)$ $-10\,SI$ unit
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$(s)$ $-5\,SI$ unit
For the velocity-time graph shown in the figure, in a time interval from $t=0$ to $t=6\,s$, match the following columns.
| Colum $I$ | Colum $II$ |
| $(A)$ Change in velocity | $(p)$ $-5 / 3\,Sl$ unit |
| $(B)$ Average acceleration | $(q)$ $-20\,SI$ unit |
| $(C)$ Total displacement | $(r)$ $-10\,SI$ unit |
| $(D)$ Acceleration at $t=3\,s$ | $(s)$ $-5\,SI$ unit |
The displacement of a particle after time $t$ is given by $x = \left( {k/{b^2}} \right)\left( {1 - {e^{ - bt}}} \right)$ where $b$ is a constant. What is the acceleration of the particle?
The displacement of a particle after time $t$ is given by $x = \left( {k/{b^2}} \right)\left( {1 - {e^{ - bt}}} \right)$ where $b$ is a constant. What is the acceleration of the particle?