A body starts from the origin with an acceleration of 6 m/s² along the x-axis and 8 m/s² along the y-axis. Its distance from the origin after 4 seconds will be

Correct Option: 80 m

To find the distance of the body from the origin after 4 seconds, we can analyze its motion independently along the x-axis and the y-axis.

1. Motion along the x-axis:
The body starts from rest at the origin, so its initial velocity along the x-axis ($u_x$) is 0.
The acceleration along the x-axis is given as $a_x=6{\text{m/s}}^2$.
Using the second equation of motion, the displacement along the x-axis ($x$) in time $t=4\text{s}$ is:

$x=u_x$

Substituting the values:

$x=0\times 4+\frac{1}{2}\times 6\times {\left(4\right)}^2$

$x=3\times 16=48\text{m}$

2. Motion along the y-axis:
Similarly, the initial velocity along the y-axis ($u_y$) is 0.
The acceleration along the y-axis is given as $a_y=8{\text{m/s}}^2$.
The displacement along the y-axis ($y$) in time $t=4\text{s}$ is:

$y=u_{y}t+\frac{1}{2}{a}_y{t}^2$

Substituting the values:

$y=0\times 4+\frac{1}{2}\times 8\times {\left(4\right)}^2$

$y=4\times 16=64\text{m}$

3. Distance from the origin:
The distance ($d$) of the body from the origin $(0,0)$ is the magnitude of the position vector:

$d=\sqrt{x^2+y^2}$

Substituting the displacements:

$d=\sqrt{{48}^2+{64}^2}$

$d=\sqrt{2304+4096}$

$d=\sqrt{6400}=80\text{m}$

Therefore, the distance of the body from the origin after 4 seconds is 80 m.