Question

A particle moves in x-y plane according to the equations $x=4t^2+5t+16$ and $y=5t$ where $x,y$ are in metre and $t$ is in second. The acceleration of the particle is:

• A. $8m/s^{-1}$
• B. $12m/s^{-1}$
• C. $14m/s^{-1}$
• D. $16m/s^{-1}$

Answer 1

The correct option is A $8m/s^{-1}$

Given,

$x=4t^2+5t+16$

$y=5t$

velocity along x-axis

$v_x=\frac{dx}{dt}=(8t+5)m/s$

acceleration along x-axis,

$a_x=\frac{v_x}{dt}=8m/s$

velocity alon y-axis

$v_y=\frac{dy}{dt}=5m/s$

acceleration along y- axis,

$a_y=\frac{v_y}{dt}=0m/s$

The acceleration of the particle is given by

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

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

$a=\sqrt{8^2+0^2}=8m/s^2$

The correct option is A.