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The relation between time and distance is $\mathrm{t}={\mathrm{\alpha x}}^2+\mathrm{\beta x}$, where $\mathrm{\alpha }$ and $\mathrm{\beta }$ are constants. The retardation is
1.  $2{\mathrm{\alpha v}}^3$
2.  $2{\mathrm{\beta v}}^3$
3.  $2{\mathrm{\alpha \beta v}}^3$
4.  $2{\mathrm{\beta }}^2{\mathrm{v}}^3$

The coordinates of a moving particle at a time t, are given by, x=5 sin 10t, y=5 cos 10t. The speed of the particle is
1.  25
2.  50
3.  10
4.  $50\sqrt{2}$

A satellite in force-free space sweeps stationary interplanetary dust at a rate dM/dt=$\mathrm{\alpha }$v where M is the mass, v is the velocity of the satellite and $\mathrm{\alpha }$ is a constant. What is the deacceleration of the satellite ?
1.  $-2{\mathrm{\alpha v}}^2/\mathrm{M}$
2.  $-{\mathrm{\alpha v}}^2/\mathrm{M}$
3.  $+{\mathrm{\alpha v}}^2/\mathrm{M}$
4.  $-{\mathrm{\alpha v}}^2$

A body of mass 3 kg is moving under a force, which causes a displacement in it, given by $\mathrm{S}=\frac{{\mathrm{t}}^3}{3}$(in m). Find the work done by the force in first 2 seconds .
1.  2 J
2.  3.8 J
3.  5.2 J
4.  24 J