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

Subtopic:  Non Uniform Acceleration |
68%
From NCERT
NEET - 2015
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A particle moves a distance $$x$$ in time $$t$$ according to equation $$x=(t+5)^{-1}.$$ The acceleration of the particle is proportional to:
1. (velocity)$$3/2$$
2. (distance)$$2$$
3. (distance)$$-2$$
4. (velocity)$$2/3$$

Subtopic:  Acceleration |
70%
From NCERT
AIPMT - 2010
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The distance travelled by a particle starting from rest and moving with an acceleration $$\frac{4}{3}$$ ms-2, in the third second is:
1. $$6$$ m
2. $$4$$ m
3. $$\frac{10}{3}$$ m
4. $$\frac{19}{3}$$ m

Subtopic:  Distance & Displacement |
79%
From NCERT
AIPMT - 2008
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A car moves from $$X$$ to $$Y$$ with a uniform speed $$v_u$$ and returns to $$X$$ with a uniform speed $$v_d.$$ The average speed for this round trip is:

 1 $$\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}$$ 2 $$\sqrt{v_{u} v_{d}}$$ 3 $$\frac{v_{d} v_{u}}{v_{d} + v_{u}}$$ 4 $$\frac{v_{u} + v_{d}}{2}$$
Subtopic:  Average Speed & Average Velocity |
82%
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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The graph of displacement time is given below.

Its corresponding velocity-time graph will be:

 1 2 3 4
Subtopic:  Graphs |
68%
From NCERT
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A particle moves along a path $$ABCD$$ as shown in the figure. The magnitude of the displacement of the particle from $$A$$ to $$D$$ is:

1. $\left(5+10\sqrt{2}\right)$m
2. $$10$$ m
3. $15\sqrt{2}$ m
4. $$15$$ m

Subtopic:  Distance & Displacement |
70%
From NCERT
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Acceleration-time graph of a body is shown.

The corresponding velocity-time graph of the same body is:

 1 2 3 4
Subtopic:  Graphs |
65%
From NCERT
PMT - 2004
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The displacement of a particle is given by $$y = a + bt + ct^{2} - dt^{4}$$. The initial velocity and acceleration are, respectively:

 1 $$b, -4d$$ 2 $$-b,2c$$ 3 $$b, ~2c$$ 4 $$2c, -2d$$
Subtopic:  Non Uniform Acceleration |
81%
From NCERT
PMT - 1999
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A point moves in a straight line under the retardation $$av^2$$${}^{}$. If the initial velocity is $$u,$$ the distance covered in $$t$$ seconds is:
1. $$(aut)$$
2. $$\frac{1}{a}\mathrm{ln}(aut)$$
3. $$\frac{1}{a}\mathrm{ln}(1+aut)$$
4. $$a~\mathrm{ln}(aut)$$

Subtopic:  Non Uniform Acceleration |
56%
From NCERT
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