For an object moving with uniform acceleration, travelling 50m in 5th sec, 70m in 7th sec

a) Its initial velocity is$5\text{m/s}$      

b) Its acceleration is$20{\text{m/s}}^2$

c) Its travels 100m in$9^{\text{th}}\sec$     

d) Its average velocity during$9^{\text{th}}\sec$ is$90\text{m/s}$

$\begin{array}{c}{\text{S}}_7=\text{u}+\text{a}\left(7-\frac{1}{2}\right)=70\Rightarrow \underset{\_}{\text{u}+\frac{13\text{a}}{2}=70}\\ \frac{4a}{2}=20\end{array}$

$\text{a}=10{\text{ms}}^{-2}$

$\text{u}+\frac{\text{9a}}{\text{2}}=50$

$\text{u}+\frac{9\left(10\right)}{2}=50$

$\text{u}=50-45=5{\text{ms}}^{-1}$

Distance travel in 9^th second

${\text{S}}_{\text{9}}=\text{u}+\text{a}\left(9-\frac{1}{2}\right)$

${\text{S}}_{\text{9}}=5+10\left(\frac{17}{2}\right)$

$=90\text{m}$

Final velocity after 8 sec

$\text{v}=\text{u}+\text{at}=\text{5}+\text{8}\times \text{10}=\text{85}$

(means during 9^th second)

Final velocity after 9 seconds

$\text{v}=\text{u}+\text{at}$

$=\text{5}+\text{10}\times \text{9}$

            $=\text{95}\text{m/s}$

            ${\overrightarrow{v}}_{\text{Avg}}=\frac{85+95}{2}=90\text{m/s}$