Question

The displacement $\left(x\right)$ of a particle along a straight line at time $t$ is given by $x=a_0+\frac{a_1}{2}t+\frac{a_2}{3}{t}^2$, the acceleration of the particle is

• A. $a_1/2$
• B. $a_2/3$
• C. $a_0+a_2/3$
• D. $2a_2/3$

Answer 1

The correct option is D $2a_2/3$

$x=(a_0+\frac{a_1}{2}t+\frac{a_2}{3}{t}^2)$
We know that $v=\frac{dx}{dt}$
$\Rightarrow v=\frac{d}{dt}(a_0+\frac{a_1}{2}t+\frac{a_2}{3}{t}^2)$
Or $v=\frac{a_1}{2}+\frac{a_2}{3}\times 2t=\frac{a_1}{2}+\frac{2a_2}{3}t$
Acceleration, $a=\frac{dv}{dt}$
$=\frac{d}{dt}(\frac{a_1}{2}+\frac{2a_2}{3}t)=\frac{2a_2}{3}$