Acceleration of a body whose displacement follows the equation $3 s=9 t+5 t^2$ is in $\mathrm{ms}^{-2}$
Acceleration of a body whose displacement follows the equation $3 s=9 t+5 t^2$ is in $\mathrm{ms}^{-2}$
$\frac{5}{3}$
$\frac{14}{3}$
$\frac{10}{3}$
$\frac{19}{3}$
Solution
Given, displacement
$3 s=9 t+5 t^2$...(i)
From second equation of motion, we get
$s=u t+\frac{1}{2} a t^2$...(ii)
Rearranging Eq. (i), we get
$s=3 t+\frac{5}{3} t^2$...(iii)
By comparing Eq. (ii) and Eq. (iii), we get
$\begin{aligned} \frac{1}{2} a & =\frac{5}{3} \\ \Rightarrow \quad a & =\frac{10}{3} \mathrm{~ms}^{-2}\end{aligned}$