Question

A body of mass $2kg$ has an initial velocity of $3m/s$ along $OE$ and it is subjected to a force of $4N$ along of direction perpendicular to $OE$ as shown in figure. The distance travelled by the body in $4s$ from $O$ will be

• A. $12m$
• B. $20m$
• C. $28m$
• D. $48m$

Answer 1

Answer: (B)

$20m$

Let $OE$ and $OY$ be along $X$ and $Y$ axis respectively,
then $u_x=3m/s,a_x=0$
and $u_y=0,a_y=\frac{4}{2}=2m/s^2$
at $t=4s$, let $S_x$ and $S_y$ be the displacement along x-axis and y-axis respectively, then
$S_x=u_x=\frac{1}{2}{a}_x{t}^2=3\times 4+\frac{1}{2}\left(0\right){\left(4\right)}^2=12m$
and
$S_y=u_{y}t+\frac{1}{2}{a}_y{t}^2=0\times 4+\frac{1}{2}\left(2\right){\left(4\right)}^2=16m$
so, the resultant displacement $S$ is given as
$S=\sqrt{{S_x}^2+{S_y}^2}=20m$