A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $\mathrm{v}\left(\mathrm{x}\right)$ $={\mathrm{\beta x}}^{-2\mathrm{n}}$ where $\mathrm{\beta }$ and $$\mathrm{n}$$ are constants and $$\mathrm{x}$$ is the position of the particle. The acceleration of the particle as a function of $$\mathrm{x}$$ is given by:
1. $-2{\mathrm{n\beta }}^{2}{\mathrm{x}}^{-2\mathrm{n}-1}$
2. $-2{\mathrm{n\beta }}^{2}{\mathrm{x}}^{-4\mathrm{n}-1}$
3. $-2{\mathrm{\beta }}^{2}{\mathrm{x}}^{-2\mathrm{n}+1}$
4. $-2{\mathrm{n\beta }}^{2}{\mathrm{x}}^{-4\mathrm{n}+1}$

Subtopic:  Non Uniform Acceleration |
68%
From NCERT
NEET - 2015
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The position of a particle with respect to time $$t$$ along the $$\mathrm{x}$$-axis is given by $$9t^{2}-t^{3}$$ where x is in metre and $$t$$ in second. What will be the position of this particle when it achieves maximum speed along the $$+\mathrm{x}$$ direction?
1. $$32$$ m
2. $$54$$ m
3. $$81$$ m
4. $$24$$ m

Subtopic:  Non Uniform Acceleration |
77%
From NCERT
AIPMT - 2007
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A particle moving along the x-axis has acceleration $$f,$$ at time $$t,$$ given by, $$f=f_0\left ( 1-\frac{t}{T} \right ),$$  where $$f_0$$ and $$T$$ are constants. The particle at $$t=0$$ has zero velocity. In the time interval between $$t=0$$ and the instant when $$f=0,$$ the particle’s velocity $$\left ( v_x \right )$$ is:
1. $$f_0T$$
2. $$\frac{1}{2}f_0T^{2}$$
3. $$f_0T^2$$
4. $$\frac{1}{2}f_0T$$

Subtopic:  Non Uniform Acceleration |
57%
From NCERT
AIPMT - 2007
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