A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time '$t$' is proportional to
(1) $t^{3/4}$
(2) $t^{3/2}$
(3) $t^{1/4}$
(4) $t^{1/2}$

A force $\vec { F } = ( 5 \hat { i } + 3 \hat { j } + 2 \hat { k } ) N$ is applied over a particle which displaces it from its origin to the point $\vec { r } = ( 2 \hat { i } - \hat { j } ) m$. The work done on the particle in joules is
(1) - 7
(2) + 7
(3) + 10
(4) + 13

A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is
(1) $40 \mathrm{~m}/\mathrm{s}$
(2) $20 \mathrm{~m}/\mathrm{s}$
(3) $10 \mathrm{~m}/\mathrm{s}$
(4) $10\sqrt{30} \mathrm{~m}/\mathrm{s}$

A body of mass 2 kg is driven by an engine delivering a constant power of $1\,\mathrm{J\,s^{-1}}$. The body starts from rest and moves in a straight line. After 9 s, the body has moved a distance (in m) ...

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time $t$ is proportional to:-
(1) $t ^ { \frac { 2 } { 3 } }$
(2) $t ^ { \frac { 3 } { 2 } }$
(3) $t$
(4) $t ^ { \frac { 1 } { 2 } }$

An automobile of mass $m$ accelerates starting from the origin and initially at rest, while the engine supplies constant power $P$. The position is given as a function of time by:
(1) $\left( \frac { 9 P } { 8 m } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 3 } { 2 } }$
(2) $\left( \frac { 8 P } { 9 m } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 2 } { 3 } }$
(3) $\left( \frac { 9 m } { 8 P } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 3 } { 2 } }$
(4) $\left( \frac { 8 P } { 9 m } \right) ^ { \frac { 1 } { 2 } } t ^ { \frac { 3 } { 2 } }$

The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x+1}}$, that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of $x$ will be
(1) 16
(2) 2
(3) 2.4
(4) 4

A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of $30 ^ { \circ }$ with horizontal with an effective acceleration of $1 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. The power delivered by the pulling force at $t = 10 \mathrm {~s}$ from the start is $\_\_\_\_$ W. [Use $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$] (Calculate the nearest integer value)