# A car moves from $$\mathrm{X}$$ to $$\mathrm{Y}$$ with a uniform speed $$\mathrm{v_u}$$ and returns to $$\mathrm{X}$$ with a uniform speed $$\mathrm{v_d}.$$ The average speed for this round trip is: 1. $\frac{2{\mathrm{v}}_{\mathrm{d}}{\mathrm{v}}_{\mathrm{u}}}{{\mathrm{v}}_{\mathrm{d}}+{\mathrm{v}}_{\mathrm{u}}}$ 2. $\sqrt{{\mathrm{v}}_{\mathrm{u}}{\mathrm{v}}_{\mathrm{d}}}$ 3. $\frac{{\mathrm{v}}_{\mathrm{d}}{\mathrm{v}}_{\mathrm{u}}}{{\mathrm{v}}_{\mathrm{d}}+{\mathrm{v}}_{\mathrm{u}}}$ 4. $\frac{{\mathrm{v}}_{\mathrm{u}}+{\mathrm{v}}_{\mathrm{d}}}{2}$

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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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 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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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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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 |
64%
From NCERT
PMT - 2004
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The displacement of a particle is given by $\mathrm{y}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^{2}-{\mathrm{dt}}^{4}$. The initial velocity and acceleration are, respectively:

 1 $$\mathrm{b}, ~\mathrm{-4d}$$ 2 $$\mathrm{-b},~ \mathrm{2c}$$ 3 $$\mathrm{b}, ~\mathrm{2c}$$ 4 $$\mathrm{2c}, ~\mathrm{-2d}$$
Subtopic:  Non Uniform Acceleration |
81%
From NCERT
PMT - 1999
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For the given acceleration $$\left ( a \right )$$ versus time $$\left ( t \right )$$ graph of a body, the body is initially at rest.

From the following, the velocity $$\left ( v \right )$$ versus time $$\left ( t \right )$$ graph will be:

 1 2 3 4

Subtopic:  Non Uniform Acceleration |
61%
From NCERT
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