Question

A body starts from the origin with an acceleration of $6m{s}^{-2}$ along the x-axis and $8m{s}^{-2}$ along the y-axis. Its distance from the origin after $4seconds$ will be

• A. $56m$
• B. $64m$
• C. $80m$
• D. $128m$

Answer 1

The correct option is C $80m$

Given:
initial velocity in X-direction = $0m{s}^{-1}$,
initial velocity in Y-direction = $0m{s}^{-1}$,
acceleration in X-direction = $6m{s}^{-2}$,
acceleration in Y-direction = $8m{s}^{-2}$,
time taken= $4seconds$,
using $2^{nd}$ law of motion,
$s=ut+\frac{1}{2}a{t}^2$
Displacement along X- axis : $x=u_{x}t+\frac{1}{2}{a}_x{t}^2=\frac{1}{2}\times 6\times (4{)}^2=48m$ Displacement along Y- axis : $y=u_{y}t+\frac{1}{2}{a}_y{t}^2=\frac{1}{2}\times 8\times (4{)}^2=64m$
Total distance from the origin $=\sqrt{x^2+y^2}=\sqrt{(48{)}^2+(64{)}^2}=80m$.