Question

The $x$ and $y$ coordinates of the particle at any time are $x=5t-2t^2$ and $y=10t$ respectively, where $x$ and $y$ are in $meters$ and $t$ in $seconds.$ The acceleration of the particle at $t=2s$ is

• A. $5m/s^2$
• B. $-4m/s^2$
• C. $-8m/s^2$
• D. $0$

Answer 1

The correct option is B $-4m/s^2$

Given,

$x=5t-2t^2$

$y=10t$

Velocity along x-axis,

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

$v_x=(5-4t)m/s$

Acceleration along x-axis,

$a_x=\frac{dv}{dt}$

$a_x=\frac{d(5-4t)}{dt}$

$a_x=-4m/s^2$

Velocity along y-axis,

$v_y=\frac{dy}{dt}=\frac{d\left(10t\right)}{dt}$

$v_y=10m/s$

Acceleration, $a_y=\frac{dy}{dt}$

$a_y=\frac{d\left(10\right)}{dt}=0m/s^2$

The net acceleration of the particle is

$\overrightarrow{a}=a_x\hat{i}+a_y\hat{j}$

$\overrightarrow{a}=-4\hat{i}+0\hat{j}$

$a=\sqrt{(-4{)}^2+(0{)}^2}=\sqrt{16}m/s^2$

$a=4m/s^2$