Question

A car starts accelerating with an acceleration of $\frac{1}{3}{\text{m/s}}^2$ when its speed was $18\text{km/h}$. If the displacement of car in $n^{th}$ minute after it starts accelerating is $4.8\text{km},$ then $n$ is:

Answer 1

Given acceleration of car is $\frac{1}{3}{\text{m/s}}^2=\frac{60\times 60}{3}{\text{m/min}}^2$
$=\frac{3600}{3}=1200{\text{m/min}}^2$
Initial velocity $=18\text{km/h}=\frac{18000}{60}=300\text{m/min}$
Using, $S=u+\frac{a}{2}(2n-1)$
$4.8\left(1000\right)=300+\frac{a}{2}(2n-1)$
$4800=300+\frac{1200}{2}(2n-1)$
$=\frac{2\times 4500}{1200}=2n-1$
$\Rightarrow n=4.2\approx 4^{th}$ minute.