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An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by $\frac{\mathrm{dv}}{\mathrm{dt}}=-2.5\sqrt{\mathrm{v}}$ where v is the instantaneous speed. The time taken by the object, to come to rest, would be
1.  2s
2.  4s
3.  8s
4.  1s

The acceleration $\mathrm{\alpha }$ of a particle starting from rest varies with time according to relation $\mathrm{a}=\mathrm{\alpha t}+\mathrm{\beta }$. The velocity of the particle after a time t will be
1.  $\frac{{\mathrm{\alpha t}}^2}{2}+\mathrm{\beta }$
2.  $\frac{{\mathrm{\alpha t}}^2}{2}+\mathrm{\beta t}$
3.  ${\mathrm{\alpha t}}^2+\frac{1}{2}\mathrm{\beta t}$
4.  $\frac{\left({\mathrm{\alpha t}}^2+\mathrm{\beta }\right)}{2}$

A body starting from rest moves with uniform acceleration. The distance covered by the body in time t is proportional to
1.  $\sqrt{\mathrm{t}}$
2.  ${\mathrm{t}}^{3/2}$
3.  ${\mathrm{t}}^{2/3}$
4.  ${\mathrm{t}}^2$

A particle moves along a straight line OX. At a time t (in second) the distance x (in metre) of the particle from O is given by $\mathrm{x}=40+12\mathrm{t}-{\mathrm{t}}^3$. How long would the particle travel before coming to rest?
1.  24 m
2.  40 m
3.  56 m
4.  16 m

A particle located at x=0 at time t=0, starts moving along the positive x-direction with a velocity v that varies as $\mathrm{v}=\mathrm{\alpha }\sqrt{\mathrm{x}}$. The displacement of the particle varies with time as
1.  ${\mathrm{t}}^2$
2.  $\mathrm{t}$
3.  ${\mathrm{t}}^{1/2}$
4.  ${\mathrm{t}}^3$

The acceleration experienced by a moving boat after its engine is cut-off, is given by $\mathrm{a}=-{\mathrm{kv}}^3$, where k is a constant. If ${\mathrm{v}}_0$ is the magnitude of velocity at cut-off, then the magnitude of the velocity at time t after the cut off is
1.  $\frac{{\mathrm{v}}_0}{2{\mathrm{ktv}}_0^2}$
2.  $\frac{{\mathrm{v}}_0}{1+2{\mathrm{ktv}}_0^2}$
3.  $\frac{{\mathrm{v}}_0}{\sqrt{1-2{\mathrm{kv}}_0^2}}$
4.  $\frac{{\mathrm{v}}_0}{\sqrt{1+2{\mathrm{ktv}}_0^2}}$

The relation between time t and distance x is $\mathrm{t}={\mathrm{ax}}^2+\mathrm{bx}$, where a and b are constants. The acceleration is
1.  $-2{\mathrm{abv}}^2$
2.  $2{\mathrm{bv}}^3$
3.  $-2{\mathrm{av}}^3$
4.  $2{\mathrm{av}}^2$

If the velocity of a particle is given by $\mathrm{v}={\left(180-16\mathrm{x}\right)}^{1/2} {\mathrm{ms}}^{-1}$, then its acceleration will be
1.  zero
2.  $8 {\mathrm{ms}}^{-2}$
3.  $-8 {\mathrm{ms}}^{-2}$
4.  $4 {\mathrm{ms}}^{-2}$

A particle moves along x-axis as $\mathrm{x}=4 \left(\mathrm{t}-2\right)+\mathrm{a}{\left(\mathrm{t}-2\right)}^2$. Which of the following is true?
1.  The initial velocity of particle is 4
2.  The acceleration of particle is 2a
3.  The particle is at origin at t=0
4.  None of the above

A particle moves along a straight line such that its displacement at any time t is given by $\mathrm{s}={\mathrm{t}}^3-6{\mathrm{t}}^2+3\mathrm{t}+4$. The velocity when its acceleration is zero is
1.  $2 {\mathrm{ms}}^{-1}$
2.  $12 {\mathrm{ms}}^{-1}$
3.   $-9 {\mathrm{ms}}^{-1}$
4.  $2 {\mathrm{ms}}^1$

A particle starts from rest at t=0 and undergoes an acceleration a in ms^-2 with time t in second which is as shown
                   
Which one of the following plot represents velocity v in ms^-1 versus time t in second?
1.
2.
3.
4.

A particle starts from rest. Its acceleration (a) versus time (t) is as shown in the figure. The maximum speed of the particle will be
                                 
1.  $110 {\mathrm{ms}}^{-1}$
2.  $55 {\mathrm{ms}}^{-1}$
3.  $550 {\mathrm{ms}}^{-1}$
4.  $660 {\mathrm{ms}}^{-1}$

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?
                           
1.
2.
3.
4.

$\mathrm{ABCDEF}$ is a regular hexagon with point O as centre. The value of $\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}$ is
1.  $2\overrightarrow{\mathrm{AO}}$
2.  $4\overrightarrow{\mathrm{AO}}$
3.  $6\overrightarrow{\mathrm{AO}}$
4.  $0$

If $\overrightarrow{\mathrm{A}}=\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{C}},$ and the magnitudes of $\overrightarrow{\mathrm{A}}, \overrightarrow{\mathrm{B}}, \overrightarrow{\mathrm{C}}$ are 5, 4 and 3 units, then angle between $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{C}}$ is
1.  ${\cos }^{-1} \left(\frac{3}{5}\right)$
2.  ${\cos }^{-1} \left(\frac{4}{5}\right)$
3.  ${\sin }^{-1} \left(\frac{3}{4}\right)$
4.  $\frac{\mathrm{\pi }}{2}$

A box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to
1.  ${\mathrm{t}}^{1/2}$
2.  ${\mathrm{t}}^{3/4}$
3.  ${\mathrm{t}}^{3/2}$
4.  ${\mathrm{t}}^2$