Question

A particle is moving in $x-y$ plane on a straight line its $x$ and $y$ coordinates are given as $x=({2t}^2+4)m$ and $Y=(\frac{\sqrt{3}x}{2}+8)m$ and $t$ is in second. The acceleration of the particle is

• A. $\sqrt{7}{m/s}^2$
• B. $\sqrt{5}{m/s}^2$
• C. $2\sqrt{7}{m/s}^2$
• D. None of these

Answer 1

The correct option is D None of these

Given,

$x=(2t^2+4)m$

$y=(\frac{\sqrt{3}t}{2}+8)m$

Velocity along x-axis,

$v_x=\frac{dx}{dt}$

$v_x=4t$

Acceleration, $a_x=\frac{d{v}_x}{dt}=4m/s^2$

Velocity along y-axis,

$v_y=\frac{dy}{dt}=\frac{\sqrt{3}}{2}$

Acceleration along y-axis,

$a_y=0m/s$

Acceleration of the particle,

$a=\sqrt{a_x^2+a_y^2}$

$a=\sqrt{(4{)}^2+(0{)}^2}$

$a=4m/s^2$