A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time $t^{\prime}$ is proportional to :

  • A

    $t^{\frac{1}{4}}$

  • B

    $t^{\frac{3}{4}}$

  • C

    $t^{\frac{3}{2}}$

  • D

    $t^{\frac{1}{2}}$

Similar Questions

Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2 m$ at rest the collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body $A$ is

A ball moving with velocity $2\, m/s$ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as, $a_c = k^2rt^2$, The power delivered to the particle by the forces acting on it is

A curved surface is shown in figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$ which is at a slightly greater height than $C$.

With the surface $AB$, ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.

$(a)$ For which balls is total mechanical energy conserved ?

$(b)$ Which ball $(s)$ can reach $D$ ?

$(c)$ For ball which do not reach $D$, which of the balls can reach back $A$ ?

A body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ..............  $\mathrm{m} / \mathrm{s}$