A particle has an initial velocity $3 \hat { i } + 4 \hat { j }$ and an acceleration of $0.4 \hat { i } + 0.3 \hat { j }$. Its speed after 10 s is
(1) 10 units
(2) $7 \sqrt { 2 }$ units
(3) 7 units
(4) 8.5 units

A particle moves from the point $( 2.0 \hat { i } + 4.0 \hat { j } ) \mathrm { m }$, at $\mathrm { t } = 0$, with an initial velocity $( 5.0 \hat { i } + 4.0 \hat { j } ) \mathrm { ms } ^ { - 1 }$. It is acted upon by a constant force which produces a constant acceleration $( 4.0 \hat { i } + 4.0 \hat { j } ) \mathrm { ms } ^ { - 2 }$. What is the distance of the particle from the origin at time 2 s ?
(1) 15 m
(2) $20 \sqrt { 2 } \mathrm {~m}$
(3) 5 m
(4) $10 \sqrt { 2 } \mathrm {~m}$

A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F _ { 0 } \left[ 1 - \left( \frac { t - T } { T } \right) ^ { 2 } \right]$ where $F _ { 0 }$ and $T$ are constants. The force acts only for the time interval $2 T$. The velocity $v$ of the particle after time $2 T$ is:
(1) $\frac { 2 F _ { 0 } T } { M }$
(2) $\frac { F _ { 0 } T } { 2 M }$
(3) $\frac { 4 F _ { 0 } T } { 3 M }$
(4) $\frac { F _ { 0 } T } { 3 M }$